Task-Based Core-Periphery Organization of Human Brain
Dynamics
Danielle S. Bassett1,2*, Nicholas F. Wymbs3, M. Puck Rombach4,5, Mason A. Porter4,5, Peter J. Mucha6,7,
Scott T. Grafton3
1 Department of Physics, University of California, Santa Barbara, Santa Barbara, California, United States of America, 2 Sage Center for the Study of the Mind, University of
California, Santa Barbara, Santa Barbara, California, United States of America, 3 Department of Psychological and Brain Sciences and UCSB Brain Imaging Center, University
of California, Santa Barbara, Santa Barbara, California, United States of America, 4 Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University
of Oxford, Oxford, United Kingdom, 5 CABDyN Complexity Centre, University of Oxford, Oxford, United Kingdom, 6 Carolina Center for Interdisciplinary Applied
Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina, United States of America, 7 Institute for Advanced Materials,
Nanoscience & Technology, University of North Carolina, Chapel Hill, North Carolina, United States of America
Abstract
As a person learns a new skill, distinct synapses, brain regions, and circuits are engaged and change over time. In this paper,
we develop methods to examine patterns of correlated activity across a large set of brain regions. Our goal is to identify
properties that enable robust learning of a motor skill. We measure brain activity during motor sequencing and characterize
network properties based on coherent activity between brain regions. Using recently developed algorithms to detect timeevolving communities, we find that the complex reconfiguration patterns of the brain’s putative functional modules that
control learning can be described parsimoniously by the combined presence of a relatively stiff temporal core that is
composed primarily of sensorimotor and visual regions whose connectivity changes little in time and a flexible temporal
periphery that is composed primarily of multimodal association regions whose connectivity changes frequently. The
separation between temporal core and periphery changes over the course of training and, importantly, is a good predictor
of individual differences in learning success. The core of dynamically stiff regions exhibits dense connectivity, which is
consistent with notions of core-periphery organization established previously in social networks. Our results demonstrate
that core-periphery organization provides an insightful way to understand how putative functional modules are linked. This,
in turn, enables the prediction of fundamental human capacities, including the production of complex goal-directed
behavior.
Citation: Bassett DS, Wymbs NF, Rombach MP, Porter MA, Mucha PJ, et al. (2013) Task-Based Core-Periphery Organization of Human Brain Dynamics. PLoS
Comput Biol 9(9): e1003171. doi:10.1371/journal.pcbi.1003171
Editor: Olaf Sporns, Indiana University, United States of America
Received February 19, 2013; Accepted June 21, 2013; Published September 26, 2013
Copyright: ! 2013 Bassett et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: DSB was supported by the Sage Center for the Study of the Mind, the Errett Fisher Foundation, the Templeton Foundation, the David and Lucile
Packard Foundation, the Public Health Service Grant NS44393, and the Institute for Collaborative Biotechnologies through Contract W911NF-09-D-0001 from the
US Army Research Office. MAP and MPR acknowledge a research award (#220020177) from the James S. McDonnell Foundation. MAP was also funded by FET
Proactive Project PLEXMATH (FP7-ICT-2011-8; Grant #317614) from the European Commission as well as by the EPSRC (EP/J001759/1). PJM acknowledges
support from Award Number R21GM099493 from the National Institute of General Medical Sciences. The content is solely the responsibility of the authors and
does not necessarily represent the official views of any of the funding agencies. The funders had no role in study design, data collection and analysis, decision to
publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: [email protected]
configuration and intelligence [6] as well as relationships between
altered brain network organization and disease [7]. In this paper,
we extend this approach to a non-stationary situation: the change
of network activity across the brain as a new skill is acquired.
Acquisition of new motor skills alters brain activity across spatial
scales. At the level of individual neurons, this induces changes in
firing behavior in the motor cortex [8]. At the level of large-scale
areas, this induces changes in the interactions between primary
motor cortex and premotor areas, and these changes can influence
the amount of learning [9]. Previous studies have demonstrated
that pairwise interactions between some of these premotor regions,
as measured by the magnitude of coherence between lowfrequency blood-oxygen-level-dependent (BOLD) signals ,
strengthen with practice [10]. Furthermore, complex contributions
by non-motor systems such as prefrontal cortex are involved in the
strategic control of behavior during learning [11]. These findings
reveal some of the changes in local circuits that occur with
Introduction
Cohesive structures have long been thought to play an
important role in information processing in the human brain
[1]. At the small scale of individual neurons, temporally coherent
activity supports information transfer between cells [2]. At a much
larger scale, simultaneously active cortical areas form functional
systems that enable behavior [1]. However, the question of
precisely what type of cohesive organization is present between the
constituents of brain systems—especially at larger scales—has
been steeped in controversy [3,4]. Although low-frequency
interactions between pairs of brain areas are easy to measure,
the simultaneous characterization of dynamic interactions across
the entire human brain remained challenging until recent
applications of network theory to neuroimaging data [5]. These
efforts have led to enormous insights, including the establishment
of relationships between stationary functional brain network
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Core-Periphery Organization of Brain Dynamics
networks [16] and summarize our findings using diagnostics that
quantify three properties of community structure. (See Materials
and Methods for their definitions and Ref. [17] for evidence
supporting the utility of these diagnostics in capturing changes in
brain dynamics over 3 days of learning.) To measure the strength
of functional modularization in the brain and quantify the extent
of compartmentalization of putative functional modules, we
maximize a quality function called multilayer modularity Q to obtain
a partition of the brain into communities. (The associated
maximum value of Q is known as the maximum modularity.) A high
value of Q indicates that the pattern of functional connectivity in
the brain can be clustered sensibly into distinct communities of
brain regions that exhibit similar time courses. We also compute
the number n of communities (i.e., putative functional modules) in
partitions of the multilayer networks. A large value of n indicates
that there are a large number of distinct temporal profiles in
BOLD activations in the brain. To measure the temporal
variability of community structure, we compute the flexibility fi of
each region i, as this quantifies the frequency that a brain region i
changes its allegiances to network communities over time. A high
value of flexibility indicates that a region often changes community
affiliation.
Our results demonstrate that the temporal evolution of
community structure is modulated strongly by the depth of
training (as reflected in the total number of practiced trials). We
also show that the temporal variability of module allegiance varies
across brain regions. Sensorimotor and visual cortices form the
bulk of a relatively stiff temporal core in which module affiliations
change little over a scanning session, whereas multimodal
association areas form the bulk of a relatively flexible temporal
periphery in which module affiliations change frequently. The
separation between the temporal core and temporal periphery
predicts individual differences in extended learning. We combine
these methods for identifying a temporal core and periphery with a
notion of core-periphery organization that originated in the social
sciences [18] to show that the organizational structure of
functional networks in 2–3 minute time windows correlates with
the organizational structure of the brain’s temporal evolution:
densely connected regions in individual time windows tend to
exhibit little change in module allegiance over time, whereas
weakly connected regions tend to exhibit significant changes.
Taken together, our results suggest that core-periphery organization is a critical property that is as important as modularity for
understanding and predicting cognition and behavior (see Fig. 1B).
Author Summary
When someone learns a new skill, his/her brain dynamically alters individual synapses, regional activity, and
larger-scale circuits. In this paper, we capture some of
these dynamics by measuring and characterizing patterns
of coherent brain activity during the learning of a motor
skill. We extract time-evolving communities from these
patterns and find that a temporal core that is composed
primarily of primary sensorimotor and visual regions
reconfigures little over time, whereas a periphery that is
composed primarily of multimodal association regions
reconfigures frequently. The core consists of densely
connected nodes, and the periphery consists of sparsely
connected nodes. Individual participants with a larger
separation between core and periphery learn better in
subsequent training sessions than individuals with a
smaller separation. Conceptually, core-periphery organization provides a framework in which to understand how
putative functional modules are linked. This, in turn,
enables the prediction of fundamental human capacities,
including the production of complex goal-directed behavior.
learning. However, there remains no global assessment of changes
in brain networks as a result of learning. In this paper, we seek to
find cohesive structures in global brain networks that capture
dynamics that are particularly relevant for characterizing skill
learning that takes place over the relatively long time scales of
minutes to hours of practice.
To address these issues, we extract a set of functional networks
from task-based functional Magnetic Resonance Imaging (fMRI)
time series that describe functional connectivity between brain
regions. We probe the dynamics of these putative interactions by
subdividing time series into discrete time intervals (of approximately two minutes in duration; see Fig. 1A) during the acquisition
of a simple motor skill. Subjects learned a set of 10-element motor
sequences similar to piano arpeggios by practicing for at least 30
days during a 6-week period. The depth of training was
manipulated so that 2 sequences were extensively practiced
(EXT), 2 sequences were moderately practiced (MOD), and 2
sequences were minimally practiced (MIN) on each day. In
addition, subjects performed blocks of all of the sequences during
fMRI scanning on approximately days 1, 14, 28, and 42 of
practice. Using the fMRI time series, we extract functional
networks representing the coherence between 112 cortical and
subcortical areas for each sequence block.
To characterize brain dynamics, we represent sets of functional
networks as multilayer brain networks and we identify putative
functional modules—i.e., groups of brain regions that exhibit
similar BOLD time courses—in each 2–3 minute time window.
Such cohesive groups of nodes are called ‘‘communities’’ in the
network-science literature [12,13], and they suggest that different
sets of brain regions might be related to one another functionally
either through direct anatomical connections or through indirect
activation by an external stimulus. A community of brain regions
might code for a different function (e.g., visual processing, motor
performance, or cognitive control), or it might engage in the same
function using a distinct processing stream. Characterizing
changes in community structure thus makes it possible to map
meaningful dynamic patterns of functional connectivity that relate
to changes in cognitive function (e.g., learning).
We employ computational tools for dynamic community
detection [14,15] for multilayer representations of temporal
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Results
Dynamic Community Structure Changes with Learning
Community structure changes with the number of trials
practiced, independent of when the practice occurred in the 6
weeks. In Fig. 2, we show multilayer modularity (Q, a measure of
the quality of a partition into communities), the number of
P
communities, and mean flexibility (F~ N1 N
i~1 fi , a measure of
the temporal variability in module allegiance) as a function of the
number of training trials completed after a scanning session. See
Materials and Methods for the definitions and Table 1 for the
relationship between the number of trials practiced and training
duration and intensity. After an initial increase from 50 to 200
trials practiced, multilayer modularity decreases with an increase
in the number of trials practiced, suggesting that community
structure in functional brain networks becomes less pronounced
with learning. Both the number of communities and the flexibility
of community structure increase with the number of trials
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Core-Periphery Organization of Brain Dynamics
Figure 1. Network organization of human brain dynamics. (A) Temporal Networks of the Human Brain. We parcellate the brain into
anatomical regions that can be represented as nodes in a network, and we use the coherence between functional Magnetic Resonance Imaging
(fMRI) time series of each pair of nodes over a time window to determine the weight of the network edge connecting those nodes. We determine
these weights separately using approximately 10 non-overlapping time windows of 2–3 min duration and thereby construct temporal networks that
represent the dynamical functional connectivity in the brain. (B) Cohesive Mesoscale Structures. (top) An example of a network with a modular
organization in which high-degree nodes (brown) are often found in the center of modules or bridging distinct modules that are composed mostly of
low-degree nodes (blue). (bottom) A network with a core-periphery organization in which nodes in the core (purple) are more densely connected
with one another than nodes in the periphery are with one another (green).
doi:10.1371/journal.pcbi.1003171.g001
practiced, which is consistent with an increased specificity of
functional connectivity patterns with extended learning.
positive values that we observe indicate that the distributions from
all participants are skewed to the right. The kurtosis of a
distribution is a combined measure of its peakedness [19] and its
bimodality [20], and it is sometimes construed as a measure of the
extent that a distribution is prone to outliers. The kurtosis values
that we observe vary between 2.5 and 5, which includes the value
of 3 that occurs for a Gaussian distribution.
Defining the temporal core and temporal periphery. To
determine the significance of a brain region’s variation in
flexibility, we compared the flexibility of brain regions in the
empirical multilayer network to that expected in a nodal null
model. We can define a temporal core, bulk, and periphery (see
Fig. 3). The core is the set of regions whose flexibility is
significantly less than expected in the null model; the periphery
is the set of regions whose flexibility is significantly greater than
expected in the null model; and the bulk consists of all remaining
regions. As discussed in the Text S1, the delineation of the brain
Temporal Core-Periphery Organization
Regional variation in flexibility. The mean flexibility over
participants varied over brain regions. It ranged from approximately 0:04 to approximately 0:14, which implies that brain
regions changed their modular affiliation between 4% and 14% of
trial blocks on average (see Fig. 3A). The distribution of flexibility
across brain regions is decidedly non-Gaussian: the majority of
brain regions have relatively high flexibilities, but there is a leftheavy tail of regions (including a small peak) with low values of
flexibility. We characterized the distribution of flexibility over
brain regions by calculating the third (skewness) and fourth
(kurtosis) central moments. The skewness was 0:50+0:26, and the
kurtosis was 3:04+0:57. To interpret these findings, we note that
a distribution’s skewness is a measure of its asymmetry, and the
Figure 2. Dynamic network diagnostics change with learning. (A) Multilayer modularity, (B) number of communities, and (C) mean flexibility
calculated as a function of the number of trials completed after a scanning session (see Table 1 for the relationship between the number of trials
practiced and training duration and intensity). We average the values for each diagnostic over the 100 multilayer modularity optimizations, and we
average flexibility over the 112 brain regions (in addition to averaging over the 100 optimizations per subject). Error bars indicate the standard error
of the mean over participants.
doi:10.1371/journal.pcbi.1003171.g002
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Table 1. Relationship between training duration, intensity,
and depth.
Session 1 Session 2
Session 3
Session 4
MIN Sequences
50
110
170
230
MOD Sequences
50
200
350
500
EXT Sequences
50
740
1430
2120
We report the number of trials (i.e., ‘‘depth’’) of each sequence type (i.e.,
‘‘intensity’’) completed after each scanning session (i.e., ‘‘duration’’) averaged
over the 20 participants.
doi:10.1371/journal.pcbi.1003171.t001
into these three groups is robust both to the intensity of training
(MIN, MOD, or EXT) and to the duration of training (sessions 1–
4). Furthermore, the temporal core, bulk, and periphery tend to
form their own communities, although the relationship between
core-periphery organization and modular organization appears to
be altered by learning (see the Text S1).
We show the anatomical locations of the temporal core,
temporal bulk, and temporal periphery in Fig. 3. The relatively
stiff core is composed of 19 regions located predominantly in
primary sensorimotor areas in both left and right hemispheres.
Most of the motor-related regions in the core were left-lateralized,
which is consistent with the participants’ use of their right hand to
perform the motor sequence. The more flexible periphery is
composed of 25 regions located predominantly in multimodal
areas—including inferior parietal, intraparietal sulcus, temporal
parietal junction, inferotemporal, fusiform gyrus, and visual
association areas. The bulk contains the remaining 68 cortical
and subcortical regions—including large swaths of frontal,
temporal, and parietal cortices. See Table S3 for a complete list
of the affiliation of each brain region to the temporal core, bulk,
and periphery. The separation of a temporally stiff core of
predominantly unimodal regions that process information from
single sensory modality (e.g., vision, audition, etc.) and a flexible
periphery of predominantly multimodal cortices that process
information from multiple modalities is consistent with existing
understanding of the association of multimodal cortex with the
binding of different types of information and the performance of a
broad range of cognitive functions [21].
Temporal core-periphery organization and learning. One
can interpret the anatomical location of the temporally stiff core
that consists primarily of unimodal regions and a flexible
periphery that consists primarily of multimodal cortices in the
context of the known roles of these cortices in similar tasks. The
ability to retrieve and rapidly execute complex motor sequences
requires extensive practice. These well-learned sequences are
known to be generated by ‘‘core’’ areas [8,22–24]. However,
when first learning a sequence, people can use a variety of
cognitive strategies that are supported by other brain systems
(some of which are located in the periphery to augment
performance) [25,26]. In some cases, these strategies are
detrimental to skill retention [27]. Consequently, we hypothesized that individuals whose core and periphery are distinct—
indicating a strong separability of visuomotor and cognitive
regions—would learn better than those whose core and periphery
were less distinguishable from one another.
To test this hypothesis, we calculated the Spearman rank
coefficient r between the skewness and kurtosis of the flexibility
distribution estimated from the fMRI data of the first scanning
session and the learning parameter k estimated over the next 10
days of home training (see Materials and Methods). The kurtosis
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Figure 3. Temporal core-periphery organization of the brain.
determined using fMRI signals during the performance of a simple
motor learning task. (A) The core (cyan), bulk (gold), and periphery
(maroon) nodes consist, respectively, of brain regions whose mean
flexibility over individuals is less than, equal to, and greater than that
expected in a null model (gray shaded region). We measure flexibility
based on the allegiance of nodes to putative functional modules. Error
bars indicate the standard error of the mean over individuals. (B) The
anatomical distribution of regions in the core, bulk, and periphery
appears to be spatially contiguous. The core primarily contains
sensorimotor and visual processing areas, the periphery primarily
contains multimodal association areas, and the bulk contains the
remainder of the brain (and is therefore composed predominantly of
frontal and temporal cortex).
doi:10.1371/journal.pcbi.1003171.g003
(in essence) measures the separation between the temporal core
and the temporal periphery and is negatively correlated with k (the
:
:
correlation is r ¼ {0:498, and the p-value is p ¼ 0:027),
indicating that individuals with a narrower separation between
temporal core and temporal periphery learn better in the
subsequent 10 home training sessions than individuals with a
greater separation between temporal core and temporal periphery.
Skewness (in essence) measures the presence of—rather than the
separation between—the temporal core and the temporal periph:
ery and is also negatively correlated with learning (r ¼ {0:480
:
and p ¼ 0:034), indicating that individuals whose flexibility was
more skewed over brain regions learned better than those whose
flexibility over brain regions was less skewed. This finding implies
that individuals with ‘‘stronger’’ temporal core-periphery structure
(i.e., larger values of skewness) learn better than those with
‘‘weaker’’ temporal core-periphery structure (i.e., smaller values of
skewness).
Importantly, the temporal separation of the data from the
scanning session (which we used to estimate brain flexibility) and
the home training (which we used to estimate learning) ensures
that these correlations are predictive. Together, these results
indicate that individuals with a stronger temporal core and
temporal periphery but a smooth transition between them seem to
learn better than individuals with a weaker temporal core and
temporal periphery but a sharper transition between them. These
results suggest that successful brain function might depend on a
delicate balance between a set of core regions whose allegiance to
putative functional modules changes little over time and a set of
peripheral regions whose allegiance to putative functional modules
is flexible through time (and also on the smoothness of the
transition between these two types of regions).
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Figure 4. Geometrical core-periphery organization in brain networks. (A) Core quality R (5) in the (a,b) parameter plane for a typical
participant (3), scanning session (1), sequence type (EXT), and experimental block (1). (B) Distribution of the a and b values that maximize the R-score.
We compute this distribution over all network layers, participants, scanning sessions, and sequence types. The b parameter is much more localized
(its standard deviation is 0.05) than the a parameter (its standard deviation is 0.26). (C) Mean core shape. We plot the ordered vector of C values. We
have set the values of a and b to the mean values of those that maximize the R-score for all network layers, participants, scanning sessions, and
sequence types.
doi:10.1371/journal.pcbi.1003171.g004
tion, we examine the distributions of the relative frequencies of a
and b values that maximize the R-score for each network layer,
participant, scanning session, and sequence type (see Fig. 4B). We
:
:
use the mean values of these distributions (a ¼ 0:40 and b ¼ 0:94)
to assign a core score to each node. In Fig. 4C, we show the shape
of the ‘‘mean core’’ that we obtain using these parameter values.
This figure demonstrates that the typical (geometrical) coreperiphery organization in the networks under study is a mixture
between a discrete core-periphery organization, in which every
node is either in the core or in the periphery, and a continuous
core-periphery organization, in which there is a continuous
spectrum to describe how strongly nodes belong to a core. In
these networks (which usually possess a single core), the majority of
nodes do not belong to the core, but those nodes that do (roughly
10% of the nodes) have a continuum level of association strengths
with the core.
In some cases, we identified multiple competing cores, which we
found by using simulated annealing to explore local maxima of the
R-score rather than only identifying a global maximum. Because
of this stochasticity in the methodology for examining coreperiphery organization, we performed computations with the
:
:
chosen parameter values (a ¼ 0:40 and b ¼ 0:94) 10 times and
used the solution with the highest R-score out of these 10 iterations
for each network layer, subject, scanning session, and sequence
type.
An interesting question is whether geometrical core-periphery
organization remains relatively constant throughout time or
whether the organization changes with learning. We observed
that regions that have a high geometrical core score in the first
scanning session and in EXT blocks were likely to have high
geometrical core scores in later scanning sessions and in MOD and
MIN blocks. (See the Text S1 for supporting results on the
reliability of geometrical core-periphery organization.) In light of
this consistency, we calculate a mean geometrical core score for
each node by taking the mean over all blocks in a given scanning
session (1, 2, 3, and 4) and sequence type (EXT, MOD, and MIN).
The variance of the mean geometrical core score over nodes in a
network then gives an indication of the separation between the
mean core and periphery. As we show in Fig. 5, we find that the
variance of the mean geometrical core score over trials decreases
as a function of learning. A high variance of the mean core scores
over nodes indicates a greater separation between the mean core
and periphery as well as a high consistency of the core score of
each node over trial blocks. If a node’s core score is inconsistent
Geometrical Core-Periphery Organization
Given our demonstration that there exists a temporal core in
dynamic brain networks, it is important to ask what role such core
regions might play in individual network layers of the multilayer
network [17]. While the roles of nodes in a static network can be
studied in multiple ways [28,29], we focus on describing the
geometrical core-periphery organization— which can be used to
help characterize the organization of edge strengths throughout a
network —to compare it with the temporal core-periphery
organization discussed above. The geometrical core of a network
is composed of a set of regions that are strongly and mutually
interconnected. Measures of network centrality can be useful for
identifying nodes in a geometrical core because such measures
help capture a node’s relative importance within a network in
terms of its immediate connections, its distance to other nodes in
the graph, or its influence on other nodes in the graph [30,31].
Drawing on studies of social networks [18], we examine
geometrical core-periphery organization in networks extracted
from individual time windows by testing whether core nodes are
densely connected to one another and whether peripheral nodes
are sparsely connected to one another. Rather than proposing a
strict separation between a single core and single periphery, we
assess the role of a node along a core-periphery spectrum using a
centrality measure known as the (geometrical) core score C, which
was introduced in Ref. [30]. Network nodes with high C values are
densely connected to one another, whereas nodes with low C
values are sparsely connected to one another. The method in Ref.
[30] uses a two-parameter function to interpolate between core
nodes and peripheral nodes. One parameter (which is denoted by
a) sets the sharpness of the boundary between the geometrical core
and the geometrical periphery. Small values of a indicate a fuzzy
boundary, whereas large values indicate a sharp transition. The
second parameter (which is denoted by b) sets the size of the
geometrical core. Smaller values of b correspond to smaller cores.
We can quantify the fit of the transition function that defines the
set of core scores to the data using a summary diagnostic that is
called the R-score (see Materials and Methods for definitions ).
Large values of R indicate a good fit and therefore provide
confidence that one has uncovered a good estimate of a network’s
core-periphery organization.
In Fig. 4A, we show a typical R-score landscape in the (a,b)
parameter plane. This landscape favors a relatively small core and
a medium value of the transition-sharpness parameter. To choose
sensible values of a and b for studying core-periphery organizaPLOS Computational Biology | www.ploscompbiol.org
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Core-Periphery Organization of Brain Dynamics
Discussion
over trial blocks, then the mean core score for each node in the
network is expected to be similar and thus one would expect the
variance of the core scores over nodes to be small. A low variance
in the mean geometrical core score over trial blocks therefore
suggests either little separation between the core and periphery or
an increased variability in core scores of a given node over trial
blocks.
We have shown how the mesoscale organization of functional
brain networks changes over the course of learning. Our results
suggest that core-periphery organization is an important and
predictive component of cognitive processes that support sequential, goal-directed behavior. We summarize our findings in Fig. 7,
which demonstrates that poor learners tend to have poorer
separation between core and periphery (as indicated by straighter,
shorter spirals in the figure) and that good learners tend to have
greater separation between core and periphery (curvier, longer
spirals). Our findings also demonstrate that during the generation
of motor sequences, the brain consists of a temporally stable and
densely connected set of core regions complemented by a
temporally flexible and sparsely connected set of peripheral
regions. This functional tradeoff between a core and periphery
might provide a balance between the rigidity necessary to
maintain motor function by the core and the adaptivity of the
periphery necessary to enable behavioral change as a function of
context or strategy.
In the Text S1, we provide supporting results that indicate (i)
that our findings are not merely a function of variation in region
size and (ii) that they cannot be derived from the underlying block
design of the experimental task. We also show in this supplement
that (arguably) simpler properties of brain function—such as the
regional signal power of brain activity, mean connectivity strength,
and parameter estimates from a general linear model—provide
less predictive power than core-periphery organization.
Relationship between Temporal and Geometrical CorePeriphery Organization
Given the geometrical core-periphery organization in the
individual layers of the multilayer networks and the temporal
core-periphery organization in the full multilayer networks, it is
important to ask whether brain regions in the temporal core (i.e.,
regions with low flexibility) are also likely to be in the geometrical
core (i.e., whether they exhibit strong connectivity with other core
nodes, as represented by a high value of the geometrical core
score). In Fig. 6, we show scatter plots of the flexibility and core
score for the 3 training levels (EXT, MOD, and MIN) and the 4
scanning sessions over the 6-week training period. We find that the
temporal core-periphery organization (which is a dynamic
measurement) is strongly correlated with the geometrical core
score (which is a measure of network geometry and hence of
network structure). This indicates that regions with low temporal
flexibility tend to be strongly-connected core nodes in (static)
network layers. In Fig. 6, we show that the relationship between
temporal and geometrical core-periphery organization occurs
reliability across training depth, duration, and intensity. In Fig. 7,
we show that this relationship can also be identified robustly in
data extracted from individual subjects.
Core-Periphery Organization of Human Brain Structure
and Function
The notion of a core-periphery organization is based on the
structure (rather than the temporal dynamics) of a network [30].
Intuitively, a core consists of a set of highly and mutually
interconnected set of regions . In this paper, we have described
what is traditionally called ‘‘core-periphery structure’’ using the
terminology geometrical core-periphery organization. (It is geometrical
rather than topological because the networks are weighted.) This
intuitive notion was formalized in social networks by Borgatti and
Everett in 1999 [18]. Available methods to identify and quantify
geometrical core-periphery organization in networks include ones
based on block models [18], k-core organization [32], and
aggregation of information about connectivity and short paths
through a network [33]. Unfortunately, many methods that have
been used to study cores and peripheries in networks have
binarized networks that are inherently weighted, which requires
one to throw away a lot of important information. Even the
recently developed weighted extensions of k-core decomposition
[34] require a discretization of k-shells, which have been defined
for both binary and weighted networks [35]. Importantly, k-core
decomposition is based on a very stringent and specific type of core
connectivity, so this measure misses important core-like structures
[30,36]. A well-known measure called the ‘‘rich-club coefficient’’
(RCC) [37] considers a different but somewhat related question of
whether nodes of high degree (defined as k§kt some threshold
value kt ) tend to connect to other nodes of high degree. (The RCC
is therefore a form of assortativity.) The RCC has also been
extended to weighted networks [38], but it still requires one to
specify a threshold value of richness to enable one to ask whether
‘‘rich’’ nodes tend to connect to other ‘‘rich’’ nodes.
The aforementioned limitations notwithstanding, several of the
measures discussed above have recently been used successfully to
identify a structural core of the human brain white-matter tract
network, which is characterized not only by a k-core with a high
Figure 5. Geometrical core scores change with learning.
Variance of the distribution of mean geometrical core scores over
brain regions as a function of the number of trials completed after a
scanning session. (See Table 1 for the relationship between the number
of trials practiced and training duration and intensity.) Error bars
indicate the standard error of the mean over participants (where the
data point from each participant is the mean geometrical core score
over brain regions, scanning sessions, sequence types, and network
layers).
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Figure 6. Relationship between temporal and geometrical core-periphery organizations. A strong negative correlation exists between
flexibility and the geometrical core score for networks constructed from blocks of (A) extensively, (B) moderately, and (C) minimally trained sequences
on scanning session 1 (day 1; circles), session 2 (after approximately 2 weeks of training; squares), session 3 (after approximately 4 weeks of training;
diamonds), and session 4 (after approximately 6 weeks of training; stars). This negative correlation indicates that the temporal core-periphery
organization is mimicked in the geometrical core-periphery organization and therefore that the core of dynamically stiff regions also exhibits dense
connectivity. We show temporal core nodes in cyan, temporal bulk nodes in gold, and temporal periphery nodes in maroon. The darkness of data
points indicates scanning session; darker colors indicate earlier scans, so the darkest colors indicate scan 1 and the lightest ones indicate scan 4. The
grayscale lines indicate the best linear fits; again, darker colors indicate earlier scans, so session 1 is in gray and session 4 is in light gray. The Pearson
correlation between the flexibility (averaged over 100 multilayer modularity optimizations, 20 participants, and 4 scanning sessions) and the
:
:
geometrical core score (averaged over 20 participants and 4 scanning sessions) is significant for the EXT (r ¼ {0:92, p ¼ 3:4|10{45 ), MOD
:
:
:
:
{49
{50
(r ¼ {0:93, p ¼ 2:2|10 ), and MIN (r ¼ {0:93, p ¼ 4:8|10 ) data.
doi:10.1371/journal.pcbi.1003171.g006
value of the degree k (in particular, k§20) [34] and rich club
[39,40] but also by a knotty center of nodes that have a high
geodesic betweenness centrality but not necessarily a high degree
[36]. A k-core decomposition has also been applied to functional
brain imaging data to demonstrate a relationship between network
reconfiguration and errors in task performance[41].
A novel approach that is able to overcome many of these
conceptual limitations is the geometrical core-score [30], which is
an inherently continuous measure, is defined for weighted
networks, and can be used to identify regions of a network core
without relying solely on their degree or strength (i.e., weighted
degree). Moreover, by using this measure, one can produce (i)
continuous results, which make it possible to measure whether a
brain region is more core-like or periphery-like; (ii) a discrete
classification of core versus periphery; or (iii) a finer discrete
division (e.g., into 3 or more groups). In addition, this method can
identify multiple geometrical cores in a network and rank nodes in
terms of how strongly they participate in different possible cores.
This sensitivity is particularly helpful for the examination of brain
networks for which multiple cores are hypothesized to mediate
multimodal integration [42]. In this paper, we have demonstrated
that functional brain networks derived from task-based data
acquired during goal-directed brain activity exhibit geometrical
core-periphery organization. Moreover, they are specifically
characterized by a straightforward core-periphery landscape that
includes a relatively small core composed of roughly 10% or so of
the nodes in the network.
In this paper, we have introduced a method and associated
definitions to identify a temporal core-periphery organization based
on changes in a node’s module allegiance over time. We have
defined the notion of a temporal core as a set of regions that
exhibit fewer changes in module allegiance over time than
expected in a dynamic-network null model. Neurobiologically,
the temporal core contains brain areas that show consistent taskbased mesoscale functional connectivity over the course of an
experiment , and it is therefore perhaps unsurprising that their
Figure 7. Core-periphery organization of brain dynamics
during learning. The relationship between temporal and geometrical
core-periphery organization and their associations with learning are
present in individual subjects. We represent this relationship using
spirals in a plane; data points in this plane represent brain regions
located at the polar coordinates (fs, {f k), where f is the flexibility of
the region, s is the skewness of flexibility over all regions, and k is the
learning parameter (see the Materials and Methods) that describes each
individual’s relative improvement between sessions. The skewness
predicts individual differences in learning; the Spearman rank
:
:
correlation is r ¼ {0:480 and p ¼ 0:034. Poor learners (straighter
spirals) tend to have a low skewness (short spirals), whereas good
learners (curvier spirals) tend to have high skewness (long spirals). Color
indicates flexibility: blue nodes have lower flexibility, and brown nodes
have higher flexibility.
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anatomical locations differ from nodes in the (k§20)-core [34]
and RCC [39,40] of the human white matter tract network. Our
approach is inspired by the following idea: although the brain uses
the function of a small subset of regions to perform a given task
(i.e., some sort of core ), a set of additional regions that are
associated more peripherally with the task might also be activated
in a transient manner. Indeed, several recent studies have
highlighted the possibility of a separation between groups of
regions that are consistently versus transiently activated during
task-related function [43,44], and they have demonstrated that
correlations between such regions can be altered depending on
their activity [43,45].
Given the very different definitions of the geometrical and
temporal cores, it is interesting that nodes in the temporal core are
also likely to be present in the geometrical core. Importantly, the
notions of temporal and geometrical core are complementary, and
they are both intuitive in the context of brain function. A set of
regions that is coherently active to perform a task (i.e., is in the
geometrical core) must remain online consistently throughout an
experiment (i.e., be in the temporal core), whereas a set of regions
that might be activated less coherently (i.e., is in the geometrical
periphery) can be utilized by separate putative functional modules
over time (i.e., it can be in the temporal periphery). This
interpretation is consistent with the notion that the anatomical
locations of the core and periphery are task-specific. Should brain
activity during other tasks also exhibit core-periphery organization, then the core and periphery of these other task networks
could consist of a different set of anatomical regions than those
observed here. A comparison of dynamic community structure
and associated mesoscale organizational properties across brain
states elicited by other tasks is outside of the scope of the present
study. However, such a study in a controlled sample with similar
time-series length and experimental task structure (e.g., trial
lengths, block lengths, and rest periods) would likely yield
important insights.
short time intervals (less than 5 minutes in fMRI; less than 100 s in
EEG) [47–49]. Although temporal variability in functional
connectivity was seen initially as a signature of measurement
noise [51], recent evidence suggests instead that it might provide
an indirect measurement of changing cognitive processes. Thus, it
might serve as a diagnostic biomarker of disease [51,52].
Moreover, such temporal variability appears to be modulated by
exogenous inputs. For example, Barnes et al. [53] demonstrated
using a continuous acquisition ‘‘rest-task-rest’’ design that endogenous brain dynamics do not return to their pre-task state until
approximately 18 minutes following task completion. Similar
results that consider other tasks have also been reported [54].
More generally, the dynamic nature of brain connectivity is likely
linked to spontaneous cortical processing, reflecting a combination
of both stable and transient communication pathways [48,49,55].
Network Predictions of Future Learning
In this study, we observed that properties of the temporal
organization of functional brain networks (e.g., on day 1 of this
experiment) can be used to predict extended motor learning (e.g.,
on the following 10 days of home training on a discrete sequenceproduction task). Our findings are consistent with two previous
studies that demonstrated a predictive connection between both
dynamic [17] and topological [56] network organization and
subsequent learning. (Note that we use the term topological because
Ref. [56] considered only unweighted networks.) Reference [17]
focused on early—rather than extended—learning of a cued
sequence-production motor task (rather than a discrete one) and
found that network flexibility on the first day of experiments
predicted learning on the second day and that flexibility on the
second day predicted learning on the third day. Reference [56]
investigated participants’ success in learning words of an artificial
spoken language and found that network properties from
individual time windows could be used to predict such success
[56]. Together with the present study, these results highlight the
potential breadth of the relationship between network organization and learning. The presence of such a relationship has now
been identified across multiple tasks, over multiple time scales, and
using both dynamic and topological network properties.
Modular versus Core-Periphery Organization
Community structure and core-periphery organization are two
types of mesoscale structures, and they can both be present
simultaneously in a network [30,36]. Moreover, both modular and
core-periphery organization can in principle pertain to different
characteristics of or constraints on underlying brain function. In
particular, the presence of community structure supports the idea
of the brain containing putative functional modules, whereas the
presence of a core-periphery organization underscores the fact that
different brain regions likely play inherently different roles in
information processing. A symbiosis between these two types of
organization is highlighted by the findings that we report in this
manuscript: the dynamic reconfiguration of putative functional
modules can be described parsimoniously by temporal coreperiphery organization, demonstrating that one type of mesoscale
structure can help to characterize another. Furthermore, the
notion that the brain can simultaneously contain functional
modules (e.g., the executive network or the default-mode network)
and regions that transiently mediate interactions between modules
is consistent with recent characterizations of attention and
cognitive control processes [46].
Methodological Considerations
Our study has focused on large-scale changes in dynamic
community structure that are correlated with learning. Finer-scale
investigations that employ alternative parcellation schemes [57–
62] with greater spatial resolution or alternative neuroimaging
techniques such as EEG or MEG [55] with greater temporal
resolution might uncover additional features that would enhance
understanding of functional network-based predictors of learning
phenomena.
Throughout this paper, we have referred to feature similarities
(which we estimated using the magnitude squared coherence)
between pairs of regional BOLD time series as functional connectivity
[63]. As appreciated in prior literature [64–66], the interpretation
of functional connectivity must be made with caution. Coherence
in the activity recorded at different brain sites does not necessitate
that those sites share information with one another to enable
cognitive processing, as they could instead indicate that those two
sites are activated by the same third party (either another brain
region or an external stimulus). In this paper, we do not distinguish
between these two possible drivers of strong inter-regional
coherence. Future studies could employ multiple estimates of
statistical associations in the form of diagnostics [67–69] and/or
models [70,71] that might uncover other sets of interactions that
Dynamic Brain Networks
It is increasingly apparent that functional connectivity in the
brain changes over time and that these changes are biologically
meaningful. Several recent studies have highlighted the temporal
variability [47–50] and non-stationarity [51] of functional brain
network organization, and both of these features are apparent over
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could predict the observed coherence structure and hence the
observed behavior.
sequences (red or green triangles) and for the MIN sequences
(orange or white stars, each of which was outlined in black). No
participant reported any difficulty viewing the different identity
cues. Feedback was presented after every block of 10 trials; this
feedback detailed the number of error-free sequences that the
participant produced and the mean time it took to complete an
error-free sequence.
Each fMRI test session was completed after approximately 10
home training sessions (see Table S1 for details of the number of
home practice sessions between scanning sessions), and each
participant participated in 3 test sessions. In addition, each
participant had a pre-training scan session that was identical to the
other test scan sessions immediately prior to the start of training
(see Fig. 9). To familiarize participants with the task, we gave a
brief introduction prior to the onset of the pre-training session. We
showed the participants the mapping between the fingers and the
DSP stimuli, and we explained the significance of the sequenceidentity cues.
To help ease the transition between each participant’s training
environment and that of the scanner, padding was placed under
his/her knees to maximize comfort. Participants made responses
using a fiber-optic response box that was designed with a similar
configuration of buttons as those found on the typical laptop used
during training. See the lower left of Fig. 8 for a sketch of the
button box used in the experiments. For instance, the center-tocenter spacing between the buttons on the top row was 20 mm
(compared to 20 mm from ‘‘G’’ to ‘‘H’’ on a recent MacBook
Pro), and the spacing between the top row and lower left ‘‘thumb’’
button was 32 mm (compared to 37 mm from ‘‘G’’ to the
spacebar on a MacBook Pro). The response box was supported
using a board whose position could be adjusted to accommodate a
participant’s reach and hand size. Additional padding was placed
under the right forearm to minimize muscle strain when a
participant performed the task. Head motion was minimized by
inserting padded wedges between the participant and the head coil
of the MRI scanner. The number of sequence trials performed
during each scanning session was the same for all participants,
except for two abbreviated sessions that resulted from technical
problems. In each case that scanning was cut short, participants
completed 4 out of the 5 scan runs for a given session. We included
data from these abbreviated sessions in this study.
Participants were tested inside of the scanner with the same
DSP task and the same 6 sequences that they performed during
training. Participants were given an unlimited time to complete
trials, though they were instructed to respond quickly but also to
maintain accuracy. Trial completion was signified by the visual
presentation of a fixation mark ‘‘+’’, which remained on the screen
until the onset of the next sequence-identity cue. To acquire a
sufficient number of events for each exposure type, all sequences
were presented with the same frequency. Identical to training,
trials were organized into blocks of 10 followed by performance
feedback. Each block contained trials belonging to a single
exposure type and included 5 trials for each sequence. Trials were
separated by an inter-trial interval (ITI) that lasted between 0 and
6 seconds (not including any time remaining from the previous
trial). Scan epochs contained 60 trials (i.e., 6 blocks) and consisted
of 20 trials for each exposure type. Each test session contained 5
scan epochs, yielding a total of 300 trials and a variable number of
brain scans depending on how quickly the task was performed. See
Table S2 for details of the number of scans in each experimental
block.
Behavioral apparatus. Stimulus presentation was controlled
during training using a participant’s laptop computer, which was
running Octave 3.2.4 (an open-source program that is very similar
Materials and Methods
Experiment and Data Acquisition
Ethics statement. Twenty-two right-handed participants (13
females and 9 males; the mean age was about 24) volunteered with
informed consent in accordance with the Institutional Review
Board/Human Subjects Committee, University of California,
Santa Barbara.
Experiment setup and procedure. We excluded two
participants from the investigation: one participant failed to
complete the experiment, and the other had excessive head
motion. Our investigation therefore includes twenty participants,
who all had normal/corrected vision and no history of neurological disease or psychiatric disorders. Each of these participants
completed a minimum of 30 behavioral training sessions as well as
3 fMRI test sessions and a pre-training fMRI session. Training
began immediately following the initial pre-training scan session.
Test sessions occurred after every 2-week period of behavioral
training, during which at least 10 training sessions were required.
The training was done on personal laptop computers using a
training module that was installed by the experimenter (N.F.W.).
Participants were given instructions for how to run the module,
which they were required to do for a minimum of 10 out of 14
days in a 2-week period. Participants were scanned on the first day
of the experiment (scan 1), and then a second time approximately
14 days later (scan 2), once again approximately 14 days later (scan
3), and finally 14 days after that (scan 4). Not all participants were
scanned exactly every two weeks; see Table S1 for details of the
number of days that elapsed between scanning sessions.
We asked participants to practice a set of 10-element sequences
that were presented visually using a discrete sequence-production
(DSP) task by generating responses to sequentially presented
stimuli (see Fig. 8) using a laptop keyboard with their right hand.
Sequences were presented using a horizontal array of 5 square
stimuli; the responses were mapped from left to right, such that the
thumb corresponded to the leftmost stimulus and the smallest
finger corresponded to the rightmost stimulus. A square
highlighted in red served as the imperative to respond, and the
next square in the sequence was highlighted immediately following
each correct key press. If an incorrect key was pressed, the
sequence was paused at the error and was restarted upon the
generation of the appropriate key press.
Participants had an unlimited amount of time to respond and to
complete each trial. All participants trained on the same set of 6
different 10-element sequences, which were presented with 3
different levels of exposure. We organized sequences so that each
stimulus location was presented twice and included neither
stimulus repetition (e.g., ‘‘11’’ could not occur) nor regularities
such as trills (e.g., ‘‘121’’) or runs (e.g., ‘‘123’’). Each training
session (see Fig. 9) included 2 extensively trained sequences
(‘‘EXT’’) that were each practiced for 64 trials, 2 moderately
trained sequences (‘‘MOD’’) that were each practiced for 10 trials,
and 2 minimally trained sequences (‘‘MIN’’) that were each
practiced for 1 trial. (See Table S1 for details of the number of
trials composed of extensively, moderately, and minimally trained
sequences during home training sessions.) Each trial began with
the presentation of a sequence-identity cue. The purpose of the
identity cue was to inform the participant what sequence they were
going to have to type. For example, the EXT sequences were
preceded by either a cyan (sequence A) or magenta (sequence B)
circle. Participants saw additional identity cues for the MOD
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Figure 8. Trial structure and stimulus-response (S-R) mapping. (A) Each trial began with the presentation of a sequence-identity cue that
remained on screen for 2 seconds. Each of the 6 trained sequences was paired with a unique identity cue. A discrete sequence-production (DSP)
event structure was used to guide sequence production. The onset of the initial DSP stimulus (thick square, colored red in the task) served as the
imperative to produce the sequence. A correct key press led to the immediate presentation of the next DSP stimulus (and so on) until the 10-element
sequence was correctly executed. Participants received a feedback ‘‘+’’ to signal that a sequence was completed and to wait (approximately 0–6
seconds) for the start of the next trial. This waiting period is called the ‘‘inter-trial interval’’ (ITI). At any point, if an incorrect key was hit, a participant
would receive an error signal (not shown in the figure) and the DSP sequence would pause until the correct response was received. (B) There was a
direct S-R mapping between a conventional keyboard or an MRI-compatible button box (see the lower left of the figure) and a participant’s right
hand, so the leftmost DSP stimulus cued the thumb and the rightmost stimulus cued the pinky finger. Note that the button location for the thumb
was positioned to the lower left to achieve maximum comfort and ease of motion.
doi:10.1371/journal.pcbi.1003171.g008
to MATLAB) in conjunction with PsychtoolBox Version 3. We
controlled test sessions using a laptop computer running MATLAB
version 7.1 (Mathworks, Natick, MA). We collected key-press
responses and response times using a custom fiber-optic button
box and transducer connected via a serial port (button box:
HHSC-1|4-L; transducer: fORP932; Current Designs, Philadelphia, PA).
Behavioral estimates of learning. Our goal was to study
the relationship between brain organization and learning. To
ensure independence of these two variables, we extracted brain
network structure during the 4 scanning sessions, and we extracted
behavioral estimates of learning in home training sessions 1–10
(approximately between days 1 and 14; see Table S1), which took
place before scanning session 2.
For each sequence, we defined the movement time (MT) as the
difference between the time of the first button press and the time of
the last button press during a single sequence. For the set of
sequences of a single type (i.e., sequence 1, 2, 3, 4, 5, or 6), we
estimated the learning rate by fitting an exponential function (plus
a constant) to the MT data [72,73] using a robust outlier
correction in MATLAB (using the function fit.m in the Curve Fitting
Toolbox with option ‘‘Robust’’ and type ‘‘Lar’’):
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MT~D1 et=k zD2 ,
ð1Þ
where t is time, k is the exponential dropoff parameter (which we
call the ‘‘learning parameter’’) used to describe the early (and fast)
rate of improvement, and D1 and D2 are real and positive constants.
The sum D1 zD2 is an estimate of the starting speed of a given
participant prior to training, and the parameter D2 is an estimate of
the fastest speed attainable by that participant after extended
training. A negative value of k indicates a decrease in MT, which is
thought to indicate that learning is occurring [74,75]. This decrease
in MT has been used to quantify learning for several decades
[76,77]. Several functional forms have been suggested for the fit of
MT [78,79], and the exponential (plus constant) is viewed as the
most statistically robust choice [79]. Additionally, the fitting
approach that we used has the advantage of estimating the rate of
learning independent of initial performance or performance ceiling.
Functional MRI (fMRI) Imaging
Imaging procedures. We acquired fMRI signals using a 3.0
T Siemens Trio with a 12-channel phased-array head coil. For
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Figure 9. Experiment timeline. Training sessions in the MRI scanner during the collection of blood-oxygen-level-dependent (BOLD) signals were
interleaved with training sessions at home. Participants first practiced the sequences in the MRI scanner during a baseline training session (top).
Following every approximately 10 training sessions (see Table S1), participants returned for another scanning session. During each scanning session, a
participant practiced each sequence for 50 trials. Participants trained at home between the scanning sessions (bottom). During each home training
session, participants practiced the sequences in a random order. (We determined a random order using the Mersenne Twister algorithm of Nishimura
and Matsumoto [101] as implemented in the random number generator rand.m of MATLAB version 7.1). Each EXT sequence was practiced for 64 trials,
each MOD sequence was practiced for 10 trials, and each MIN sequence was practiced for 1 trial.
doi:10.1371/journal.pcbi.1003171.g009
interactions between brain areas, it is common to apply a
standardized atlas to raw fMRI data [7,80,81]. The choice of
atlas or parcellation scheme is the topic of several recent studies in
structural [57,60], resting-state [58], and task-based [59] network
architecture. The question of the most appropriate delineation of
the brain into nodes of a network is an open one and is guided by
the particular scientific question at hand [5,61].
Consistent with previous studies of task-based functional
connectivity during learning [15,17,82] , we parcellated the brain
into 112 identifiable cortical and subcortical regions using the
structural Harvard-Oxford (HO) atlas (see Table S3) installed with
the FMRIB (Oxford Centre for Functional Magnetic Resonance
Imaging of the Brain) Software Library (FSL; Version 4.1.1)
[83,84]. For each individual participant and each of the 112
regions, we determined the regional mean BOLD time series by
separately averaging across all of the voxels in that region.
Within each HO-atlas region, we constrained voxel selection to
voxels that are located within an individual participant’s gray
matter. To do this, we first segmented each individual participant’s
T1 into white and gray matter volumes using the DARTEL
toolbox supplied with SPM8. We then restricted the gray-matter
voxels to those with an intensity of 0.3 or more (the maximum
intensity was 1.0). Note that units are based on an arbitrary scale.
We then spatially normalized the participant T1 and corresponding gray matter volume to the MNI-152 template—using the
standard SPM 12-parameter affine registration from the native
each scan epoch, we used a single-shot echo planar imaging
sequence that is sensitive to BOLD contrast to acquire 37 slices per
repetition time (TR of 2000 ms, 3 mm thickness, 0.5 mm gap)
with an echo time (TE) of 30 ms, a flip angle of 90 degrees, a field
of view (FOV) of 192 mm, and a 64|64 acquisition matrix.
Before the collection of the first functional epoch, we acquired a
high-resolution T1-weighted sagittal sequence image of the whole
brain (TR of 15.0 ms, TE of 4.2 ms, flip angle of 9 degrees, 3D
acquisition, FOV of 256 mm, slice thickness of 0.89 mm, and
256|256 acquisition matrix).
fMRI data preprocessing. We processed and analyzed
functional imaging data using Statistical Parametric Mapping
(SPM8, Wellcome Trust Center for Neuroimaging and University
College London, UK). We first realigned raw functional data, then
coregistered it to the native T1 (normalized to the MNI-152
template with a re-sliced resolution of 3|3|3 mm), and finally
smoothed it using an isotropic Gaussian kernel of 8 mm full-width
at half-maximum. To control for potential fluctuations in signal
intensity across the scanning sessions, we normalized global
intensity across all functional volumes.
Network Construction
Partitioning the brain into regions of interest. Brain
function is characterized by spatial specificity: different portions of
the cortex emit different, task-dependent activity patterns. To
study regional specificity of the functional time series and putative
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participant and scanning session. We combined the matrices in
each set separately to form a rank-3 adjacency tensor A per
sequence type, participant, and scan. Such a tensor can be used to
represent a time-dependent network [14,17]. In the following
sections, we describe a variety of diagnostics that can be used to
characterize such multilayer structures.
images to the MNI-152 template image—and resampled to 3 mm
isotropic voxels. We then restricted the voxels for each HO region
by using the program fslmaths [83,84] to include only voxels that
are in the individual participant’s gray-matter template.
Wavelet decomposition. Brain function is also characterized
by frequency specificity. Different cognitive and physiological
functions are associated with different frequency bands, and this
can be investigated using wavelets. Wavelet decompositions of
fMRI time series have been applied extensively in both restingstate and task-based conditions [85,86]. In both cases, they provide
sensitivity for the detection of small signal changes in nonstationary time series with noisy backgrounds [87]. In particular,
the maximum-overlap discrete wavelet transform (MODWT) has
been used extensively in connectivity investigations of fMRI [88–
93]. Accordingly, we used MODWT to decompose each regional
time series into wavelet scales corresponding to specific frequency
bands [94].
We were interested in quantifying high-frequency components
of an fMRI signal, correlations between which might be indicative
of cooperative temporal dynamics of brain activity during a task.
Because our sampling frequency was 2 seconds (1 TR = 2 sec),
wavelet scale one provides information on the frequency band
0.125–0.25 Hz and wavelet scale two provides information on the
frequency band 0.06–0.125 Hz. Previous work has indicated that
functional associations between low-frequency components of the
fMRI signal (0–0.15 Hz) can be attributed to task-related
functional connectivity, whereas associations between high-frequency components (0.2–0.4 Hz) cannot [95]. This frequency
specificity of task-relevant functional connectivity is likely due at
least in part to the hemodynamic response function, which might
act as a noninvertible band-pass filter on underlying neural activity
[95]. Consistent with our previous work [17], we examined
wavelet scale two, which is thought to be particularly sensitive to
dynamic changes in task-related functional brain architecture.
Construction of dynamic networks. For each of the 112
brain regions, we extracted the wavelet coefficients of the mean
time series in temporal windows given by trial blocks (of
approximately 60 TRs; see Table S2). The leftmost temporal
boundary of each window was equal to the first TR of an
experimental trial block, and the rightmost boundary was equal to
the last TR in the same block. We thereby extracted block-specific
data sets from the EXT, MOD, and MIN sequences (with 6–10
blocks of each sequence type; see Table S2 for details of the
number of blocks of each sequence type) for each of the 20
participants participating in the experiment and for each of the 4
scanning sessions.
For each block-specific data set, we constructed an N|N
adjacency matrix W representing the complete set of pairwise
functional connections present in the brain during that window in
a given participant and for a given scan. Note that N~112 is the
number of brain regions in the full brain atlas (see the earlier
section on ‘‘Partitioning the Brain into Regions of Interest’’ for
further details). To quantify the weight Wij of functional
connectivity between regions labeled i and j, we used the
magnitude squared spectral coherence as a measure of nonlinear
functional association between any two wavelet coefficient time
series (consistent with our previous study [17]). In using the
coherence, which has been demonstrated to be useful in the
context of fMRI neuroimaging data [95], we were able to measure
frequency-specific linear relationships between time series.
To examine changes in functional brain network architecture
during learning, we constructed multilayer networks by considering the set of L adjacency matrices constructed from consecutive
blocks of a given sequence type (EXT, MOD, or MIN) in a given
PLOS Computational Biology | www.ploscompbiol.org
Network Examination
Dynamic community detection. Community detection
[12,13] can be used to identify putative functional modules (i.e.,
sets of brain regions that exhibit similar trajectories through time).
One such technique is based on the optimization of the modularity
quality function [96–98]. This allows one to identify groups that
consist of nodes that have stronger connections among themselves
than they do to nodes in other groups [12]. Recently, the
modularity quality function has been generalized so that one can
consider time-dependent or multiplex networks using multilayer
modularity [14]
Q~
"
$
1 X#!
Aijl {cl Pijl dlr zdij vjlr d(gil ,gjr ),
2m ijlr
ð2Þ
where the adjacency matrix of layer l has components Aijl , the
element Pijl gives the components of the corresponding matrix for
a null model, cl is the structural resolution parameter of layer l, the
quantity gil gives the community (i.e., ‘‘module’’) assignment of
node i in layer l, the quantity gjr gives the community assignment
of node j in layer r, the parameter vjlr is the connection strength—
i.e., ‘‘interlayer coupling parameter’’, which gives an element of a
tensor w that constitutes a set of temporal resolution parameters if one is
using the adjacency tensor A to represent a time-dependent
network—between node j in layer r and node j in layer l, the total
P
edge weight in the network is m~ 12 jr kjr , the strength of node j
in layer l is kjl ~kjl zcjl , the intra-layer strength of node j in layer
l is k
jl , and the inter-layer strength of node j in layer l is
P
cjl ~ r vjlr . We employ the Newman-Girvan null model within
each layer by using
Pijl ~
kil kjl
,
2ml
ð3Þ
P
where ml ~ 12 ij Aijl is the total edge weight in layer l. We let
vjlr :v~ constant for neighboring layers (i.e., when Dl{rD~1)
and vjlr ~0 otherwise. We also let cl ~c~constant . In the main
text, we report results for v~1 and c~1, and we evaluate the
dependence of our results on c and v in the Text S1.
Optimization of multilayer modularity (2) yields a partition of
the brain regions into communities for each time window. To
measure changes in the composition of communities across time
(i.e., across experimental blocks), we defined the flexibility fi of a
node i to be the number of times that a node changed community
assignment throughout the set of time windows represented by the
multilayer network [17] normalized by the total number of
changes that were possible (i.e., by the number of contiguous pairs
of layers in the multilayer framework, which in this study ranged
from 4 to 10; see Table S2). We then defined the flexibility of the
entire network as the mean flexibility over all nodes in the
P
network: F ~ N1 N
i~1 fi . To examine the relationship between
brain network flexibility and learning, we confined ourselves to the
two EXT (i.e., extensively trained) sequences, in which learning
occurs more rapidly than in MOD and MIN sequences. We
therefore estimated flexibility from the multilayer networks
12
September 2013 | Volume 9 | Issue 9 | e1003171
Core-Periphery Organization of Brain Dynamics
constructed from blocks of the two EXT sequences in the first
scanning session.
Identification of temporal core, bulk, and periphery. We
find that different brain regions have different flexibilities. To
determine whether a particular brain region is more or less
flexible than expected, we constructed a nodal null model, which
can be used to probe the individual roles of nodes in a network
[15,17]. (Note that alternative null models can be used to probe
other aspects of the temporal or geometrical structure in a
multilayer network [15,17].) We rewired the ends of the
multilayer network’s inter-layer edges (which connect nodes in
one layer to nodes in another) uniformly at random. After
applying the associated permutation, an inter-layer edge can, for
example, connect node i in layer t with node j=i in layer tz1
rather than being constrained to connect each node i in layer t
with itself in layer tz1.
We considered 100 different rewirings to construct an ensemble
of 100 nodal null-model multilayer networks for each single
multilayer network constructed from the brain data. We then
estimated the flexibility of each node in each nodal null-model
network. We created a distribution of expected mean nodal
flexibility values by averaging flexibility over 100 rewirings and the
20 participants. We similarly estimated the mean nodal flexibility
of the brain data by averaging flexibility over the 20 participants
and 100 optimizations. (We optimized multilayer modularity using
a Louvain-like locally greedy method [99,100]. This procedure is
not deterministic, so different runs of the optimization procedure
can yield slightly different partitions of a network.) We considered
a region to be a part of the temporal ‘‘core’’ if its mean nodal
flexibility was below the 2.5% confidence bound of the null-model
distribution, and we considered a region to be a part of the
temporal ‘‘periphery’’ if its mean nodal flexibility was above the
97.5% confidence bound of the null-model distribution. Finally,
we considered a region to be a part of the temporal ‘‘bulk’’ if its
mean nodal flexibility was between the 2.5% and 97.5%
confidence bounds of the null-model distribution.
Geometrical core-periphery organization. To estimate
the geometrical core-periphery organization of the (static)
networks defined by each experimental block (i.e., for each layer
of a multilayer network), we used the method that was recently
proposed in Ref. [30]. This method results in a ‘‘core score’’
(which constitutes a centrality measure) for each node that
indicates where it lies on a continuous spectrum of roles between
core and periphery. This method has numerous advantages over
previous formulations used to study core-periphery organization.
In particular, it can identify multiple geometrical cores in a
network, which makes it possible to take multiple cores into
account and in turn enables one to construct a detailed description
of geometrical core-periphery organization by ranking the nodes
in terms of how strongly they participate in different possible cores.
Importantly, the continuous nature of the measure removes the
need to use an artificial dichotomy of being strictly a core node
versus strictly a peripheral node.
In applying method, we consider a vector C with non-negative
values, and we let Cij ~Ci |Cj , where i and j are two nodes in an
N-node network. We then seek a core vector C that satisfies the
normalization condition
X
Cm$ ~
m[f1, . . . ,Ng:
ð4Þ
We seek a permutation that maximizes the core quality
R~
X
i,j
Aij Ci Cj :
ð5Þ
This method to compute core-periphery organization has two
parameters: a[½0,1& and b[½0,1&. The parameter a sets the
sharpness of the boundary between the geometrical core and the
geometrical periphery. The value a~0 yields the fuzziest
boundary, and a~1 gives the sharpest transition (i.e., a binary
transition): as a varies from 0 to 1, the maximum slope of C $ varies
from 0 to z?. The parameter b sets the size of the geometrical
core: as b varies from 0 to 1, the number of nodes included in the
core varies from N to 0. One now has the choice of either taking
into account the local core scores of a node for a set of (a,b)
coordinates sampled from ½0,1&|½0,1& (where one weighs each
choice by its corresponding value of R) or one can take into
account only the score for particular choices of (a,b).
Statistics and Software
We performed all data analysis and statistical tests in MATLAB.
We performed the dynamic community detection procedure using
freely available MATLAB code [99] that optimizes multilayer
modularity using a Louvain-like locally greedy algorithm [100].
Supporting Information
Figure S1 Reliability of temporal core-periphery structure. Temporal core (cyan), bulk (gold), and periphery (maroon)
of dynamic networks determined based on the flexibility of trial
blocks in which participants practiced sequences that would
eventually be extensively trained. (A) Flexibility of the temporal
core, bulk, and periphery averaged over the 100 multilayer
modularity optimizations and 20 participants for blocks composed
of extensively trained (EXT; light circles), moderately trained
(MOD; squares), and minimally trained (MIN; dark diamonds)
sequences. The darkness of data points indicates scanning session;
darker colors indicate earlier scans, so the darkest colors indicate
scan 1 and the lightest ones indicate scan 4. (B) The coefficient of
variation of flexibility calculated over the 100 optimizations and 3
sequence types for all brain regions. Error bars indicate the
standard error of the mean CV over participants. Both panels use
data from scanning session 1 on day 1 of the experiment (which is
prior to home training).
(EPS)
Figure S2 Temporal core-periphery organization over
42 days. Temporal core (cyan), bulk (gold), and periphery
(maroon) of dynamic networks defined by trial blocks in which
participants practiced sequences that would eventually be (A)
extensively trained, (B) moderately trained, and (C) minimally
trained for data from scanning sessions 2 (after approximately 2
weeks of training; circles), 3 (after approximately 4 weeks of
training; squares), and 4 (after approximately 6 weeks of training;
diamonds). The darkness of data points indicates scanning session;
darker colors indicate earlier scans, so the darkest colors indicate
scan 1 and the lightest ones indicate scan 4.
(EPS)
Ci Cj ~1
i,j
and is a permutation of the vector C $ whose components specify
the local (geometrical) core values
PLOS Computational Biology | www.ploscompbiol.org
1
,
1zexpf{(m{Nb)|tan(pa=2)g
Geometrical core-periphery organization
over 42 days. Geometrical core scores for each brain region
Figure S3
13
September 2013 | Volume 9 | Issue 9 | e1003171
Core-Periphery Organization of Brain Dynamics
Figure S8 Effect of temporal resolution parameter. (A)
Number of communities averaged over 100 multilayer modularity
optimizations and over 20 participants as a function of the
temporal resolution parameter v. (B) Number of regions that we
identified as part of the temporal core (cyan; circles), temporal bulk
(gold; squares), and temporal periphery (maroon; diamonds) as we
vary v from 0:1 to 2 in increments of Dv~0:1.
(EPS)
defined by the trial blocks in which participants practiced sequences
that would eventually be (A) extensively trained, (B) moderately
trained, and (C) minimally trained for data from scanning sessions 1
(day 1; black circles), 2 (after approximately 2 weeks of training; dark
gray squares), 3 (after approximately 4 weeks of training; gray
diamonds), and 4 (after approximately 6 weeks of training; light gray
stars). We have averaged the geometrical core scores over blocks
and over 20 participants. The order of brain regions is identical for
all 3 panels (A–C), and we chose this order by ranking regions from
high to low geometrical core scores from the EXT blocks on
scanning session 1 (on day 1 of the experiment).
(EPS)
Table S1 Experimental details for behavioral data
acquired between scanning sessions. We give the minimum, mean, maximum, and standard error of the mean over
participants for the following variables: the number of days
between scanning sessions; the number of practice sessions
performed at home between scanning sessions; and the number
of trials composed of extensively, moderately, and minimally
trained sequences during home practice between scanning
sessions.
(PDF)
Figure S4 Relationship between temporal core-periphery
organization and community structure. (A) Mean-coherence
matrix over all EXT blocks from all participants on scanning day 1.
The colored bars above the matrix indicate the 3 communities that
we identified from the representative partition. Mean partition
similarity z-score zi over all participants for blocks of (B) extensively,
(C) moderately, and (D) minimally trained sequences for all 4
scanning sessions over the approximately 6 weeks of training. The
horizontal gray lines in panels (B–D) indicate the zi value that
corresponds to a right-tailed p-value of 0:05.
(EPS)
Table S2 Experimental details for brain imaging data
acquired during scanning sessions. In the top three rows,
we give the mean, minimum, maximum, and standard error over
participants for the number of blocks composed of extensively,
moderately, and minimally trained sequences during scanning
sessions. In the bottom three rows, we give (in TRs) the mean,
minimum, maximum, and standard error of the length over blocks
composed of extensively, moderately, and minimally trained
sequences during scanning sessions.
(PDF)
Region size is uncorrelated with flexibility.
(A) Scatter plot of the size of the brain region in voxels (averaged
over participants) versus the flexibility of the EXT multilayer
networks, which we averaged over the 100 multilayer modularity
optimizations and the 20 participants. Data points indicate brain
regions. The line indicates the best linear fit. Its Pearson
:
correlation coefficient is r ¼ {0:009, and the associated p-value
:
is p ¼ 0:92. (B) Box plot over the 20 participants of the squared
Pearson correlation coefficient r2 between the participant-specific
region size in voxels and the participant-specific flexibility
averaged over the 100 multilayer modularity optimizations.
(EPS)
Figure S5
Table S3 Brain regions in the Harvard-Oxford (HO)
cortical and subcortical parcellation scheme provided
by FSL [83,84] and their affiliation to the temporal core (C;
cyan), bulk (B; gold), and periphery (P; maroon) for both left (L)
and right (R) hemispheres.
(PDF)
Text S1 Supplementary materials for ‘‘Task-Based
Core-Periphery Organization of Human Brain Dynamics’’. In this document, we provide additional results to
demonstrate the reliability of temporal core-periphery organization, the reliability of geometrical core-periphery organization,
and the relationship between temporal core-periphery organization and community structure. We also include a length section on
important methodological considerations.
(PDF)
Figure S6 Temporal core-periphery organization and
task-related activations. Mean GLM parameter estimates for
the temporal core (cyan; circles), bulk (gold; squares), and
periphery (maroon; diamonds) of dynamic networks defined by
the trial blocks in which participants practiced sequences that
would eventually be (A) extensively trained, (B) moderately
trained, and (C) minimally trained for data from scanning sessions
1 (first day of training), 2 (after approximately 2 weeks of training),
3 (after approximately 4 weeks of training), and 4 (after
approximately 6 weeks of training).
(EPS)
Acknowledgments
Figure S7 Effect of structural resolution parameter.
We thank Jean M. Carlson, Matthew Cieslak, John Doyle, Daniel
Greenfield, and Megan T. Valentine for helpful discussions; John Bushnell
for technical support; and James Fowler, Sang Hoon Lee, and Melissa
Lever for comments on earlier versions of the manuscript.
(A,B) Number of communities and (C,D) number of regions in the
temporal core (cyan; circles), temporal bulk (gold; squares), and
temporal periphery (maroon; diamonds) as a function of the
structural resolution parameter c, where we considered (A,C)
c[½0:2,5& in increments of Dc~0:2 and (B,D) c[½0:8,1:8& in
increments of Dc~0:01. We averaged the values in panels (A) and
(B) over 100 multilayer modularity optimizations and over the 20
participants.
(EPS)
Author Contributions
Conceived and designed the experiments: NFW STG. Performed the
experiments: NFW STG. Analyzed the data: DSB NFW MPR.
Contributed reagents/materials/analysis tools: DSB NFW MPR MAP
PJM STG. Wrote the paper: DSB NFW MPR MAP PJM STG.
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September 2013 | Volume 9 | Issue 9 | e1003171
Text S1: Supplementary Materials for “Task-Based Core-Periphery
Organization of Human Brain Dynamics”
Danielle S. Bassett1,2,⇤ , Nicholas F. Wymbs5 , M. Puck Rombach3,4 ,
Mason A. Porter3,4 , Peter J. Mucha6,7 , Scott T. Grafton5
1 Department
of Physics, University of California, Santa Barbara, CA 93106, USA;
2
Sage Center for the Study of the Mind,
University of California, Santa Barbara, CA 93106;
3
Oxford Centre for Industrial and Applied Mathematics,
Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK;
4 CABDyN
5 Department
Complexity Centre, University of Oxford, Oxford, OX1 1HP, UK;
of Psychological and Brain Sciences and UCSB Brain Imaging Center,
University of California, Santa Barbara, CA 93106, USA;
6 Carolina
Center for Interdisciplinary Applied Mathematics,
Department of Mathematics, University of North Carolina,
Chapel Hill, NC 27599, USA;
7 Institute
for Advanced Materials, Nanoscience & Technology,
University of North Carolina, Chapel Hill, NC 27599, USA;
⇤ Corresponding
author. Email address: [email protected]
July 29, 2013
1
Reliability of Temporal Core-Periphery Organization
A brain region’s role in the temporal core, bulk, and periphery is robust across levels of training. Regions
identified as part of the core, bulk, or periphery in multilayer networks constructed from the EXT blocks in
scanning session 1 have similar flexibilities in the other two levels of training (MOD and MIN; see Fig. S1A)
for the same scanning session. To quantify the variability of a brain region’s flexibility, we calculated the
coefficient of variation (CV) of flexibility over the 100 optimizations and the 3 levels of training (see Fig. S1B).
The CV is defined as CV = /µ, where is the standard deviation of a given sample and µ is its mean. We
observe that the variabilities over optimizations and scans (i.e., CV) and over participants (i.e., error bars)
are largest in regions designated as part of the temporal core and smallest in regions designated as part of
the temporal periphery.
In addition, regional flexibility is also conserved across both intensity of training (MIN, MOD, and EXT)
and duration of training (sessions 1–4). Observe in Fig. S2 that regions identified as part of the temporal
core in multilayer networks constructed from the EXT blocks in scanning session 1 exhibit small flexibility
for all other scanning sessions and for all 3 training levels (EXT, MOD, and MIN). Regions in the temporal
bulk and temporal periphery exhibit a similar amount of flexibility to one another.
Reliability of Geometrical Core-Periphery Organization
As we illustrate in Fig. S3, the geometrical core-periphery organization of the brain was consistent over
the 42 days of practice, across sequence types, and throughout variations in the intensity of training (MIN,
MOD, and EXT) and in the duration of training (sessions 1–4).
Relationship Between Temporal Core-Periphery Organization and Community Structure
The division of the brain networks into temporal core, bulk, and peripheral nodes has interesting similarities
to their partitioning into communities based on optimizing multilayer modularity. We first noted this similarity when we examined community structure in an object that we call the mean-coherence matrix. The
mean-coherence matrix Ā contain elements Āij that are equal to the mean coherence between nodes i and
j over participants and EXT blocks on day 1 of the experiment. We determined the community structure
of this mean-coherence matrix by optimizing the single-layer modularity quality function [1, 2, 3, 4, 5]:
X
ki kj
(gi , gj ) ,
(1)
Qsingle layer =
Āij
2m
ij
where node i is assigned to community gi , node j is assigned to community gj , the Kronecker delta (gi , gj ) =
1 if gi = gj and it equals 0 otherwise, ki is the strength of node i, and m is the mean strength of all nodes in
the network. After optimizing this single-layer quality function 100 times, we constructed a representative
partition [6] from the set of 100 partitions. (Each partition arises from a single optimization.) One community
in this representative partition, which we show in Fig. S4A, appears to have high connectivity to the other
two communities: nodes in this first community have edges with strong weights to nodes in the other two
communities. This indicates a high coherence in the BOLD time series, and this behavior is consistent with
the behavior expected from a network “core”. A second community in this representative partition appears
to have low connectivity to the other two communities: nodes in this community have edges with small
weights that connect to nodes in the other two communities. This indicates a low coherence in the BOLD
time series, and this behavior is consistent with the behavior expected from a “periphery”.
It is important to note that we observed this relationship between temporal core-periphery organization
and community structure in networks encoded by mean matrices. However, networks encoded by mean matrices constructed by averaging correlation-based matrices often do not adequately represent the topological
or geometrical structure of the ensemble of individual networks from which they are derived [7]. We therefore
test for a relationship between the temporal core-periphery organization and community structure in the
ensemble of networks extracted from individual participants.
A division of the brain into temporal core, bulk, and peripheral regions gives a partition of the functional
brain network. We label this partition using the Greek letter ⌫, and we use the z-score of the Rand coefficient
[8] to test for similarities between this partition and algorithmic partitions, which we label using ⌘, into
2
communities (based on optimization of multilayer modularity) for each participant, block, and optimization.
For each pair of partitions ⌫ and ⌘, we calculate the Rand z-score in terms of the total number of node pairs
M in the network, the number of pairs M⌫ that are in the same community in partition ⌫ but not in the
partition ⌘, the number of pairs M⌘ that are in the same community in partition ⌘ but not in ⌫, and the
number of node pairs w⌫⌘ that are assigned to the same community in both partition ⌫ and partition ⌘. The
z-score of the Rand coefficient allows one to compare partitions ⌘ and ⌫, and it is given by the formula
z⌫⌘ =
1
w⌫⌘
w⌫⌘
M⌫ M⌘
,
M
(2)
where w⌫⌘ is the standard deviation of w⌫⌘ . Let the mean partition similarity z i denote the mean value of
z⌫⌘ over all partitions ⌘ (i.e., for all blocks and all optimizations) for participant i.
As we show in Fig. S4B-D, we find that communities identified by the optimization of the multilayer modularity quality function (see the “Materials and Methods” section in the main manuscript) have significant
overlap with the division into temporal core, bulk, and periphery during early learning. The mean values
of z i over participants indicate that there is a significant similarity between the partitions into modules and
the partitions into core, bulk, and periphery for networks representing functional connectivity during blocks
of extensively, moderately, and minimally trained sequences on scanning day 1. This similarity between
community structure and temporal core-periphery organization is also evident for blocks of moderately and
minimally trained sequences practiced during later scanning sessions. These results underscore the fact that
core-periphery organization can be consistent with community structure. Note, however, that there is no
statistical similarity between partitions into core, bulk, and periphery and partitions into communities for
later learning. (As shown in Fig. S4B-D, the z-scores for networks that represent the functional connectivity
during extensive training in scans 2–4, moderate training in scans 3–4, and minimal training in scan 4 are not
significantly greater than expected (i.e., under the null hypothesis of no di↵erence between the partitions).)
Together, this set of results suggests that the relationship between these two types of mesoscale organization
can be altered by learning.
Methodological Considerations
Experimental Factors
E↵ect of Region Size
Recent studies have noted that brain-region size can a↵ect estimates of hard-wired connectivity strength
used in constructing structural connectomes [9, 10]. Although the present work is concerned with functional
connectomes, it is nevertheless relevant to consider whether or not region size could be a driving e↵ect of
the observed core-periphery organization. Importantly, we observe no significant correlation between region
size and flexibility (see Fig. S5), which suggests that region size is not driving the reported results.
E↵ect of Block Design
Another important factor is the underlying experimental block design and its e↵ect on the correlation
structure between brain regions in a single time window (i.e., in a single layer in the multilayer formalism).
Two brain regions, such as motor cortex (M1) and supplementary motor area (SMA), might be active during
the trial but quiet during the inter-trial interval (ITI). This would lead to a characteristic on-o↵ activity
pattern that is highly correlated with all other regions that also turn on with the task and o↵ during the
ITI. The frequency of this task-related activity (one on-o↵ cycle per trial, where each trial is of length 4–6
TRs) is included in our frequency band of interest (wavelet scale two, whose frequency range is 0.06–0.12
Hz), and it therefore likely plays a role in the observed correlation patterns between brain regions in a single
time window.
Note, however, that our investigations of dynamic network structure—namely, our computations of flexibility of community allegiance—probe functional connectivity dynamics at much larger time scales, and the
associated frequencies are an order of magnitude smaller. They lie in the range 0.0083–0.012 Hz, as there
is one time window every 40–60 TRs. At these longer time scales, we can probe the e↵ects of both early
learning and extended learning independently of block-design e↵ects.
3
Specificity of Dynamic Network Organization as a Predictor of Learning
An important consideration is whether there exist (arguably) simpler properties of brain function than
flexibility that could be used to predict learning. We find that the power of activity, the mean connectivity
strength, and parameter estimates from a general linear model (GLM) provide less predictive power than
flexibility.
Measures of Activity and Connectivity. It is far beyond the scope of this study to perform exhaustive
computations using all possible measures of brain-region activity, so we focus on two common diagnostics.
One is based on functional connectivity, and the other is based on brain activity. To estimate the strength of
functional connectivity, we calculated the mean pairwise coherence between regional wavelet scale-two time
series constructed from the BOLD signal, where we took the mean over all possible pairs of regions and all
EXT experimental blocks extracted from scans on day 1 for a given subject. To estimate the strength of
activity, we calculated the mean signal power of the regional wavelet scale-two time series constructed from
the BOLD signal, where we took the mean over all regions and all EXT experimental blocks extracted from
scans on day 1 for a given subject. We estimate the power Pw2 of the wavelet scale-two time series as the
square of the time series normalized by its length:
Pw 2 =
X w2 (t)2
t
T
,
(3)
where T is the length of the time series [11, 12].
We found that neither mean pairwise coherence nor mean power of regional activity measured during the
first scanning session could be used to predict learning during the subsequent 10 home training sessions. For
.
.
the mean pairwise coherence, we obtained a Pearson correlation of r = 0.003 and a p-value of p = 0.987.
.
.
For the mean power of brain-region activity, we obtained r = 0.218 and p = 0.354. These results indicate
that a prediction similar to that made using the flexibility is not possible using the (arguably) simpler
properties of the mean pairwise coherence or the mean power of regional brain activity. They also suggest
that the dynamic pattern of coherent functional brain activity is more predictive than means of such activity
patterns.
Parameter Estimates for a General Linear Model. We determined relative di↵erences in the BOLD
signal by using a GLM approach for event-related functional data [13, 14]. For each participant, we constructed a single design matrix for event-related fMRI by specifying the onset time and duration of all
stimulus events from each scanning session (i.e., the pre-training session and the 3 test sessions). We found
estimations of changes in the BOLD signal related to experimental conditions by using the design matrix
with the GLM. We modeled the duration of each sequence trial as the time elapsed to produce the entire
sequence; in other words, we calculated the movement time (MT), which is a direct measure of the time
spent on a task and leads to accurate modeling of BOLD signals using the GLM [15]. Separate stimulus
vectors indicate each sequence exposure type (EXT, MOD, and MIN) for each scanning session. We took
potential di↵erences in brain activity due to rate of movement into account by using the MT for each trial as
the modeled duration for the corresponding event. We convolved events using the canonical hemodynamic
response function and temporal derivative. Using the canonical hemodynamic response function (HRF) and
its temporal derivative — we use the implementation in the Statistical Parametric Mapping Toobox (SPM8)
[18] — we then modeled the events that were specified in the stimulus vectors. From this procedure, we
obtained a pair of beta images for each event type. These images correspond to estimates of the HRF and
its temporal derivative. Using freely available software [16], we then combined the corresponding beta image
pairs for each event type (HRF and its temporal derivative) at the voxel level to form a magnitude image
[17]
q
H = sign(B̂1 ) +
(B̂1 + B̂2 ) ,
(4)
where H is called the “combined amplitude” of the estimation of the BOLD signal using the HRF (B̂1 ) and
its temporal derivative (B̂2 ). 1 This yielded separate magnitude images for each sequence exposure type
1 In this equation, we use the hat notation to indicate that these values are estimated (rather than directly measured) from
a general linear model for a response variable (such as regional cerebral blood) at each voxel in a given participant [14].
4
(EXT, MOD, and MIN) and session. We then calculated the mean region-based magnitude for each exposure
type and session using regions derived from each subject’s grey matter-constrained Harvard-Oxford (HO)
atlas.
We did not find a significant correlation between the mean parameter estimates averaged over brain
regions for the EXT trials in scanning session 1 and learning of the EXT sequences over the subsequent
.
.
approximately 10 home training sessions. The Pearson correlation is r = 0.10 and the p-value is p = 0.65.
Subject State-Dependence of Dynamic Network Organization
Our finding that temporal core-periphery organization predicts the rate of learning across individuals is
compelling evidence that the relationship between geometrical and temporal core-periphery organization is
related to learning. Nevertheless, it is important to ask whether changes in dynamic community structure
and associated mesoscale network organization are related to tasks or to changes in subjects’ physiological
state over the course of longitudinal imaging [18]. It is clear from studies of behavior, peripheral physiology,
and fMRI that subjects can have high levels of anxiety or stress (particularly during their first exposure to
MRI) [19]. To address this issue, we describe additional evidence that supports our conclusions that the
reported changes in dynamic community structure with learning are indeed related to motor tasks.
First, we note that we observed temporal and geometrical core-periphery organization consistently over
all 4 scanning sessions. In Fig. S2 of the present document, we show that the anatomical identity of nodes
in the temporal core, bulk, and periphery are consistent over scanning sessions. In Fig. S3 of this document,
we show that the anatomical identity of nodes in the geometrical core and periphery are also consistent over
scanning sessions. Moreover, Fig. 6 in the main manuscript shows that we observe the relationship between
temporal and geometrical core-periphery organization consistently across scanning sessions.
Second, we assume that the e↵ects of a subject’s mental and physiological state (e.g., anxiety) are greatest
during the first imaging session [20]. If this is indeed the case, then there could be significant changes of
network organization between scans 1 (higher anxiety) and 2 (lower anxiety) that might lead to a spurious
interpretation of changes in core-periphery organization. To examine this possibility, we test whether the
changes in dynamic community structure and core-periphery organization with learning are robust to the
removal of scan 1. Importantly, the trends in Figs. 2 and 5 in the main manuscript remain present if we only
examine scans 2–4. We use data from scan 1 for the three box plots located at the point in the horizontal
axis at which the number of trials is equal to 50. (This is the leftmost point of each panel.) See Table 1 in
the main manuscript. The 9 box plots located at points on the horizontal axis at which the number of trials
is greater than 50 use data from scans 2–4. Therefore, when we examine only scans 2–4, we still observe a
decrease in maximum modularity, an increase in the number of communities, an increase in flexibility, and
a decrease in the variance of the geometrical core score with learning.
Finally, task-related fMRI BOLD activation magnitude in core, bulk, and peripheral brain regions are
not altered significantly across scanning sessions. We employed a repeated-measures analysis of variance
(ANOVA) on the training-depth-averaged GLM parameter estimates [21]. We treated core, bulk, and periphery designations as categorical factors, and we treated scanning session as a repeated measure. We found a sig.
nificant main e↵ect (i.e., single-factor e↵ect) of core, bulk, and periphery (an F-statistic [21] of F (2, 38) = 7.88
.
.
.
and a p-value of p = 0.00137) and a non-significant e↵ect of scanning session (F (3, 57) = 0.615, p = 0.584).
These results suggest that a systematic change in the hemodynamic response function across scanning sessions is unlikely to be responsible for the observed learning-related changes in dynamic community structure.
Furthermore, we observe that mean GLM parameter estimates in core, bulk, and peripheral brain regions
are not correlated significantly with the reported changes in core-periphery structure that accompany learning. The Pearson correlation coefficient between parameter estimates and the variance of the geometrical
.
.
core score for nodes in the temporal core is r = 0.20 (which gives a p-value of p = 0.52), for nodes in the
.
.
.
.
temporal bulk is r = 0.05 (so p = 0.86), and for nodes in the temporal periphery is r = 0.52 (so p = 0.08).
These results provide further evidence that BOLD activation magnitude and dynamic community structure
provide distinct insights.
Temporal Core-Periphery Organization and Task-Related Activations
One of the strengths of our approach is that we examine the organization of whole-brain functional connectivity and thereby remain sensitive to a wide variety of learning-related changes in the brain that could not
5
be identified using a traditional GLM analysis. Nevertheless, it is useful to explore the relationship between
dynamic community structure and task-related activations. In Fig. S6, we show that regions in the temporal
core tend to be regions with strong task-related activations, as evinced by high (and positive) values of
mean GLM parameter estimates. Conversely, regions in the temporal bulk and periphery tend to lack strong
task-related activations, as evinced by low (and negative) values of mean GLM parameter estimates. These
results are consistent with our interpretation that the temporal core consists of a small set of regions that
are required to perform a given task and that the temporal periphery consists of a set of regions that are
associated more peripherally with the task and which are activated in a transient manner.
Dynamic Community Detection
In the multilayer modularity quality function (see the “Materials and Methods” section of the main manuscript),
we need to choose values for two parameters [6]: a structural resolution parameter and a temporal resolution
parameter !. We now examine the e↵ects of these choices on our results.
E↵ect of Structural Resolution Parameter
In the main manuscript, we used a structural resolution parameter value of = 1, which is the most common
choice when optimizing the single-layer and multilayer modularity quality functions [4, 5, 22]. In this case,
A
P = A P, and one is simply subtracting the optimization null model P from the adjacency tensor
A. One can decrease to access community structure at smaller spatial scales (i.e., to examine smaller
communities) or increase it to access community structure at larger spatial scales (i.e., to examine larger
communities). By examining network diagnostics over a range of values, we explore the spatial specificity
of our results.
The mean number of communities in the partitions that we obtained by optimizing multilayer modularity
Q varies from the minimum (1) to the maximum (112) possible value for approximately in the interval
[0.8, 2.5] (see Fig. 7A). We investigate this transition in greater detail in Figs. 7C,D. Near the value = 1, the
number of regions in the bulk dips to about 65, whereas the number of regions in the core and periphery rise to
about 20 and 25, respectively. Observe the dip of the bulk curve and bumps of the core and periphery curves in
Fig. 7D. These features occur for approximately in the interval [0.88, 1.22], which corresponds to partitions
that are composed of between approximately 3 and approximately 20 communities (with an associated mean
community size of between approximately 6 and approximately 37 brain regions; see Fig. 7B). This supports
our claim that the temporal core-periphery structure that we examine in this study is a genuine mesoscale
feature of coherent brain dynamics.
E↵ect of Temporal Resolution Parameter
In the main manuscript, we used a temporal resolution parameter value of ! = 1. The value ! = 1 ensures
that the inter -layer coupling is equal to the maximum possible value of the intra-layer coupling, which
we compute from the magnitude-squared coherence (which is constrained to lie in the interval [0, 1]). It
is important to examine the robustness of results for di↵erent values of this parameter, and investigating
dynamic network structure at other values of ! can also provide additional insights [6]. For example, one can
decrease ! to encourage greater variability in community assignments of nodes across individual layers (i.e.,
across time in temporal networks) or increase it to encourage such community assignments to be more similar
across layers. Recall that each node in the temporal multilayer network represents a single brain region at a
specified time, and di↵erent nodes that represent the same brain region at di↵erent times become more likely
to be assigned to the same multilayer community as ! is increased. By examining network diagnostics over
a range of ! values, we can quantify the robustness of our results to di↵ering amounts of temporal variation
in community structure.
We varied ! from 0.1 to 2 in increments of ! = 0.1. As expected, we find that the number of communities
identified in the optimization of the multilayer modularity quality function decreases as ! is increased (see
Fig. 8A). This is consistent with the fact that greater variation of community assignments across time is
possible for smaller values of !. Variation between community assignments of nodes in individual layers
can occur in two ways: (1) a small number of regions change community membership from one layer to the
next, but the majority of regions retain their community membership; or (2) entire communities lose their
6
identities (via fragmentation, extinction, union, and/or recombination), such that the algorithm identifies
either the “death” of a community that was present in the previous layer but is not present in the current
layer or the “birth” of a community that was not present in the previous layer but is present in the current
layer.
For each value of !, we examined the robustness of our division of brain regions into a temporal core, a
temporal bulk, and a temporal periphery using the same procedure that we employed for ! = 1. Namely,
we defined a temporal core and temporal periphery as those brain regions that were composed, respectively,
of the brain regions below and above the 95% confidence interval of the nodal null model. In Fig. 8B, we
report the number of regions in each group as a function of !. Interestingly, the number of brain regions that
we identified as part of the temporal core varied little over the examined range of ! values; it remained at
approximately 17.0±1.1. In fact, 15 of the 17 regions that we identified as part of the temporal core at ! = 1
were also identified as part of the temporal core at all other values of ! that we examined. The number of
regions in the temporal bulk and temporal periphery varied more (with values of approximately 75.6 ± 7.4
for the bulk and approximately 19.4 ± 6.8 for the periphery), which suggests that the separation between
the temporal bulk and temporal periphery is less drastic than that between temporal core and temporal
bulk. Indeed, the mean flexibility of the core is less similar to the mean flexibility of the bulk than is the
latter to the mean flexibility of the periphery. See Fig. 3 of the main manuscript and Figs. S1 and S2 of this
supplement.
7
Figure S1. Reliability of Temporal Core-Periphery Structure. Temporal core (cyan), bulk (gold),
and periphery (maroon) of dynamic networks determined based on the flexibility of trial blocks in which
participants practiced sequences that would eventually be extensively trained. (A) Flexibility of the temporal core, bulk, and periphery averaged over the 100 multilayer modularity optimizations and 20 participants
for blocks composed of extensively trained (EXT; light circles), moderately trained (MOD; squares), and
minimally trained (MIN; dark diamonds) sequences. The darkness of data points indicates scanning session;
darker colors indicate earlier scans, so the darkest colors indicate scan 1 and the lightest ones indicate scan
4. (B) The coefficient of variation of flexibility calculated over the 100 optimizations and 3 sequence types
for all brain regions. Error bars indicate the standard error of the mean CV over participants. Both panels
use data from scanning session 1 on day 1 of the experiment (which is prior to home training).
Figure S2. Temporal Core-Periphery Organization Over 42 Days. Temporal core (cyan), bulk
(gold), and periphery (maroon) of dynamic networks defined by trial blocks in which participants practiced
sequences that would eventually be (A) extensively trained, (B) moderately trained, and (C) minimally
trained for data from scanning sessions 2 (after approximately 2 weeks of training; circles), 3 (after approximately 4 weeks of training; squares), and 4 (after approximately 6 weeks of training; diamonds). The
darkness of data points indicates scanning session; darker colors indicate earlier scans, so the darkest colors
indicate scan 1 and the lightest ones indicate scan 4.
Figure S3. Geometrical Core-Periphery Organization Over 42 Days. Geometrical core scores for
each brain region defined by the trial blocks in which participants practiced sequences that would eventually be (A) extensively trained, (B) moderately trained, and (C) minimally trained for data from scanning
sessions 1 (day 1; black circles), 2 (after approximately 2 weeks of training; dark gray squares), 3 (after approximately 4 weeks of training; gray diamonds), and 4 (after approximately 6 weeks of training;
light gray stars). We have averaged the geometrical core scores over blocks and over 20 participants. The
order of brain regions is identical for all 3 panels (A-C ), and we chose this order by ranking regions from
high to low geometrical core scores from the EXT blocks on scanning session 1 (on day 1 of the experiment).
Figure S4. Relationship Between Temporal Core-Periphery Organization and Community Structure. (A) Mean-coherence matrix over all EXT blocks from all participants on scanning day 1. The colored
bars above the matrix indicate the 3 communities that we identified from the representative partition. Mean
partition similarity z-score zi over all participants for blocks of (B) extensively, (C) moderately, and (D)
minimally trained sequences for all 4 scanning sessions over the approximately 6 weeks of training. The
horizontal gray lines in panels (B-D) indicate the zi value that corresponds to a right-tailed p-value of 0.05.
Figure S5. Region Size is Uncorrelated with Flexibility. (A) Scatter plot of the size of the brain
region in voxels (averaged over participants) versus the flexibility of the EXT multilayer networks, which
we averaged over the 100 multilayer modularity optimizations and the 20 participants. Data points indicate
.
brain regions. The line indicates the best linear fit. Its Pearson correlation coefficient is r = 0.009, and
.
the associated p-value is p = 0.92. (B) Box plot over the 20 participants of the squared Pearson correlation
coefficient r2 between the participant-specific region size in voxels and the participant-specific flexibility
averaged over the 100 multilayer modularity optimizations.
Figure S6. Temporal Core-Periphery Organization and Task-Related Activations. Mean GLM
parameter estimates for the temporal core (cyan; circles), bulk (gold; squares), and periphery (maroon;
diamonds) of dynamic networks defined by the trial blocks in which participants practiced sequences that
would eventually be (A) extensively trained, (B) moderately trained, and (C) minimally trained for data
from scanning sessions 1 (first day of training), 2 (after approximately 2 weeks of training), 3 (after approximately 4 weeks of training), and 4 (after approximately 6 weeks of training).
Figure S7. E↵ect of Structural Resolution Parameter. (A,B) Number of communities and (C,D)
8
number of regions in the temporal core (cyan; circles), temporal bulk (gold; squares), and temporal periphery (maroon; diamonds) as a function of the structural resolution parameter , where we considered (A,C)
2 [0.2, 5] in increments of
= 0.2 and (B,D) 2 [0.8, 1.8] in increments of
= 0.01. We averaged the
values in panels (A) and (B) over 100 multilayer modularity optimizations and over the 20 participants.
Figure S8. E↵ect of Temporal Resolution Parameter. (A) Number of communities averaged over
100 multilayer modularity optimizations and over 20 participants as a function of the temporal resolution
parameter !. (B) Number of regions that we identified as part of the temporal core (cyan; circles), temporal
bulk (gold; squares), and temporal periphery (maroon; diamonds) as we vary ! from 0.1 to 2 in increments
of ! = 0.1.
9
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10
Days
Between Scans 1 and 2
Between Scans 2 and 3
Between Scans 3 and 4
Practice Sessions
Between Scans 1 and 2
Between Scans 2 and 3
Between Scans 3 and 4
Extensively Trained Trials
Between Scans 1 and 2
Between Scans 2 and 3
Between Scans 3 and 4
Moderately Trained Trials
Between Scans 1 and 2
Between Scans 2 and 3
Between Scans 3 and 4
Minimally Trained Trials
Between Scans 1 and 2
Between Scans 2 and 3
Between Scans 3 and 4
Mean
Minimum
Maximum
Standard Error
12.00
12.45
12.10
9
10
9
14
14
22
0.34
0.29
0.63
9.70
9.75
10.05
8
4
7
10
14
13
0.14
0.44
0.32
620.80
624.00
643.20
512
256
448
640
896
832
9.40
28.57
20.48
97.00
97.50
100.50
80
40
70
100
140
130
1.46
4.46
3.20
9.70
9.75
10.05
8
4
7
10
14
13
0.14
0.44
0.32
Table S1: Experimental Details for Behavioral Data Acquired Between Scanning Sessions. We
give the minimum, mean, maximum, and standard error of the mean over participants for the following
variables: the number of days between scanning sessions; the number of practice sessions performed at home
between scanning sessions; and the number of trials composed of extensively, moderately, and minimally
trained sequences during home practice between scanning sessions.
Extensively Trained Blocks
During Scan 1
During Scan 2
During Scan 3
During Scan 4
Moderately Trained Blocks
During Scan 1
During Scan 2
During Scan 3
During Scan 4
Minimally Trained Blocks
During Scan 1
During Scan 2
During Scan 3
During Scan 4
Length of Extensively Trained Blocks
During Scan 1
During Scan 2
During Scan 3
During Scan 4
Length of Moderately Trained Blocks
During Scan 1
During Scan 2
During Scan 3
During Scan 4
Length of Minimally Trained Blocks
During Scan 1
During Scan 2
During Scan 3
During Scan 4
Minimum
Mean
Maximum
Standard Error
6.00
10.00
10.00
8.00
9.70
10.00
10.00
9.90
10.00
10.00
10.00
10.00
0.21
0.00
0.00
0.10
5.00
10.00
10.00
8.00
9.70
10.00
10.00
9.90
11.00
10.00
10.00
10.00
0.27
0.00
0.00
0.10
7.00
10.00
10.00
8.00
9.80
10.00
10.00
9.90
11.00
10.00
10.00
10.00
0.18
0.00
0.00
0.10
52.50
35.50
35.40
34.60
61.94
42.36
40.79
40.30
72.20
45.90
45.50
45.70
1.34
0.72
0.77
0.87
50.80
39.70
37.60
37.60
61.67
47.56
45.07
43.83
72.60
57.20
52.80
50.60
1.26
0.80
0.67
0.79
52.10
44.10
42.50
39.70
61.19
50.02
47.37
45.79
70.60
57.70
54.50
54.10
1.29
0.73
0.71
0.70
Table S2: Experimental Details for Brain Imaging Data Acquired During Scanning Sessions.
In the top three rows, we give the mean, minimum, maximum, and standard error over participants for the
number of blocks composed of extensively, moderately, and minimally trained sequences during scanning
sessions. In the bottom three rows, we give (in TRs) the mean, minimum, maximum, and standard error of
the length over blocks composed of extensively, moderately, and minimally trained sequences during scanning
sessions.
Region Name
Affiliation
Region Name
Affiliation
Frontal pole
B(R)
B(L)
Cingulate gyrus, anterior
B(R)
B(L)
Insular cortex
B(R)
B(L)
Cingulate gyrus, posterior
P(R)
B(L)
Superior frontal gyrus
B(R)
B(L)
Precuneus cortex
B(R)
B(L)
Middle frontal gyrus
B(R)
B(L)
Cuneus cortex
C(R)
C(L)
Inferior frontal gyrus, pars triangularis
B(R)
P(L)
Orbital frontal cortex
B(R)
B(L)
Inferior frontal gyrus, pars opercularis
B(R)
B(L)
Parahippocampal gyrus, anterior
B(R)
B(L)
Precentral gyrus
C(R)
C(L)
Parahippocampal gyrus, posterior
B(R)
P(L)
Temporal pole
B(R)
B(L)
Lingual gyrus
C(R)
C(L)
Superior temporal gyrus, anterior
B(R)
B(L)
Temporal fusiform cortex, anterior
P(R)
B(L)
Superior temporal gyrus, posterior
B(R)
B(L)
Temporal fusiform cortex, posterior
P(R)
P(L)
Middle temporal gyrus, anterior
B(R)
B(L)
Temporal occipital fusiform cortex
P(R)
P(L)
Middle temporal gyrus, posterior
B(R)
B(L)
Occipital fusiform gyrus
P(R)
P(L)
Middle temporal gyrus, temporooccipital
P(R)
P(L)
Frontal operculum cortex
B(R)
P(L)
Inferior temporal gyrus, anterior
B(R)
B(L)
Central opercular cortex
B(R)
B(L)
Inferior temporal gyrus, posterior
B(R)
B(L)
Parietal operculum cortex
P(R)
B(L)
Inferior temporal gyrus, temporooccipital
B(R)
B(L)
Planum polare
C(R)
B(L)
Postcentral gyrus
P(R)
C(L)
Heschl’s gyrus
C(R)
C(L)
Superior parietal lobule
B(R)
C(L)
Planum temporale
B(R)
B(L)
Supramarginal gyrus, anterior
B(R)
C(L)
Supercalcarine cortex
C(R)
C(L)
Supramarginal gyrus, posterior
B(R)
P(L)
Occipital pole
C(R)
B(L)
Angular gyrus
P(R)
B(L)
Caudate
P(R)
B(L)
Lateral occipital cortex, superior
P(R)
P(L)
Putamen
P(R)
B(L)
Lateral occipital cortex, inferior
P(R)
B(L)
Globus pallidus
P(R)
B(L)
Intracalcarine cortex
C(R)
C(L)
Thalamus
P(R)
P(L)
Frontal medial cortex
B(R)
B(L)
Nucleus Accumbens
B(R)
B(L)
Supplemental motor area
C(R)
C(L)
Parahippocampal gyrus
B(R)
B(L)
Subcallosal cortex
B(R)
B(L)
Hippocampus
B(R)
B(L)
Paracingulate gyrus
B(R)
B(L)
Brainstem
B(R)
B(L)
Table S3: Brain regions in the Harvard-Oxford (HO) Cortical and Subcortical Parcellation Scheme provided
by FSL [83, 84] and their affiliation to the temporal core (C; cyan), bulk (B; gold), and periphery (P; maroon) for both left
(L) and right (R) hemispheres.
A
B
scan 1
2.5
0.12
0.08
0.04
core
0
extensive
bulk
periphery
40
80
120
brain region
moderate
minimal
coefficient of variation
flexibility
0.16
scan 1
2
1.5
1
0.5
0 core
0
bulk
periphery
40
80
120
brain region
A
extensive training
B
C
moderate training
minimal training
flexibility
0.18
0.14
0.1
0.06
core
0
bulk
periphery
40
80
120
brain region
0
40
80
brain region
scan 2
scan 3
120 0
scan 4
40
80
brain region
120
B
0.5
0.4
0.3
0.2
0.1
0
0
50
brain region
100
moderate training
0.5
0.4
0.3
0.2
0.1
0
C
geometrical core score
extensive training
geometrical core score
geometrical core score
A
0
scan 1
50
brain region
scan 2
100
scan 3
minimal training
0.5
0.4
0.3
0.2
0.1
0
scan 4
0
50
brain region
100
40
60
80
100
20 40 60 80 100
brain regions
C
8
7
6
5
4
3
2
1
0
1
2
3
4
scanning session
8
7
6
5
4
3
2
1
0
1
D
z−score
z−score
moderate training
extensive training
B
z−score
brain regions
20
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
mean squared coherence
A
2
3
4
scanning session
minimal training
8
7
6
5
4
3
2
1
0
1
2
3
4
scanning session
A
B
0.16
Pearson r 2
flexibility
0.14
0.12
0.1
0.08
0.06
0.04
0
500 1000 1500 2000
region size (number of voxels)
0.04
0.03
0.02
0.01
0
0.5
B
core
0
bulk
−0.5
periphery
−1
1
2
3
scanning session
4
moderate training
1
C
mean parameter estimates
extensive training
1
mean parameter estimates
mean parameter estimates
A
0.5
0
−0.5
−1
1
2
3
scanning session
4
minimal training
1
0.5
0
−0.5
−1
1
2
3
scanning session
4
B
number of communities
number of communities
A
100
80
60
40
20
0
80
60
40
20
0
0.8
1
1.2 1.4 1.6 1.8
structural resolution parameter
0
1
2
3
4
5
structural resolution parameter
D
number of regions
100
80
core
bulk
periphery
60
40
20
0
0
1
2
3
4
5
structural resolution parameter
100
number of regions
C
100
80
60
40
20
0
0.8
1
1.2 1.4 1.6 1.8
structural resolution parameter
number of communities
7
6
5
4
3
2
0
0.5
1
1.5
2
temporal resolution parameter
B
core
bulk
periphery
100
number of regions
A
80
60
40
20
0
0
0.5
1
1.5
2
temporal resolution parameter